final report cover - · 2007-11-30 · final report (pre-coat) sao binospec contract # sk4-04002...

Subsidiary of SSG Precision Optronics

FINAL REPORT (pre-coat)

SAO Binospec Contract # SK4-04002

July 21, 2006

J. Daniel 1 7/16/06

SAO Binospec Metrology Report

Jay Daniel 7/17/06

J. Daniel 2 7/16/06

Table of Contents 1. Overview and Summary ................................................................................................ 3 2. As Built Lens Parameters............................................................................................... 3 3. Spherical Surface Roughness......................................................................................... 4 4. Spherical Surface Figure Error and Lens Element Transmitted WaveFront Error........ 4 5. Slope Error Calculations and Results ............................................................................ 5 6. Optical Axis Position, TIR of Cylinder, TIR of Spherical Surface ............................... 7 7. Deviation of Aspheric Surfaces from Nominal ............................................................. 7 8. Comparison of Profilometry Derived Aspheric Best Fit Prescription to Ray Trace Results

..................................................................................................................................... 14 9. Additional Information On Drawing Note Callouts .................................................... 17 10. Radius of Curvature Measurements........................................................................... 18 11. Error Analysis Associated with the DMI Measurement for Radius of Curvature of the

Spherical Surface ........................................................................................................ 19 12. Error Associated with Profilometry for Radius of Curvature.................................... 24 13. Comparison of DMI ROC and Profilometry ROC: ................................................... 26 14. A and B datum definition........................................................................................... 27 15. Optical Test Method for establishing Optical axis angle/centration.......................... 28 16. TIR of Cylinder to Datum B ...................................................................................... 29 17. Axial Runout of Spherical Surface with Respect to Datum B................................... 30 18. Physical Runout of Surfaces ...................................................................................... 32

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1. Overview and Summary This document contains information on the metrology characteristics of the Binospec aspheric optics. All specifications are compliant except for the runout of the spherical surfaces with respect to datum B. Data is summarized in section 6 of this report, and a detailed writeup of the analysis is done in section 17. The aspheric surfaces of the elements were processed to yield optimum transmitted wavefront performance for the respective lens element. In doing so, the as built aspheric surfaces were polished to different best fit prescriptions than the nominal drawing aspheric prescriptions. The difference was characterized by measuring the sagita associated with the as-built radii and A4 deformation terms of the aspheric surfaces. These as built values are listed in table 1 in section 2. The differences in sag from the nominal print aspheric equation to the best fit aspheric surface sag were as small as 2 um P-V and as large as 12um P-V. The plots of sag deviation from print nominal, and print outs of the sag values are shown in section 7. Slope data is reported in section 5 of the report. The slopes reported are for the transmitted wavefront measurement. Surface slopes are not reported, as intended by SAO. Individual surface tests for the aspheric surfaces were not built for this project, and with good homogeneity glass, and well polished spherical surfaces, the slopes in the transmitted wavefront data represent well the slope contribution of the aspheric surfaces. The report is formatted to contain key data values for the aspheres as summary tables in the first sections. Explanation and justification of methods is contained in the later sections of the report, and surface images and data sheets are appended at the end of the report.

2. As Built Lens Parameters Table 1 contains the as built parameters for the lens spherical radii, aspheric surface best fit prescription, and center thicknesses.

BINS-1001 SN1 SN2 CommentsCenter Thickness (mm) 15.364 ± 0.0013 15.347 ± 0.0013Spherical surface radius (mm) 209.2477±7e-4 209.2523±7e-4 Value derived from DMI measurement from catseye to COCAspheric base radius (mm) 493.0660 492.9540 Value derived from profilometry and confirmed with ray trace analysisAspheric A4 (1/mm^3) 9.54457E-10 9.53020E-10 Value derived from profilometry and confirmed with ray trace analysisAspheric A6 (1/mm^5) 6.17861E-15 6.17861E-15 Print value. Not floated in any optimization.Aspheric A8 (1/mm^7) 3.80667E-19 3.80667E-19 Print value. Not floated in any optimization.P-V residual profilometry fit (μm) 0.16 0.10 Profilometry residual error after fitting R and A4 of aspheric surface.

BINS-1008 SN1 SN2Center Thickness (mm) 16.787 ± 0.0013 16.871 ± 0.0013Spherical surface radius (mm) 2223.42±0.6 2223.45±0.6 Value derived from profilometry and confirmed with test plate.Aspheric base radius (mm) -646.2724 -646.1080 Value derived from profilometry and confirmed with ray trace analysisAspheric A4 (1/mm^3) -3.70580E-09 -3.70268E-09 Value derived from profilometry and confirmed with ray trace analysisAspheric A6 (1/mm^5) -3.47213E-14 -3.47213E-14 Print value. Not floated in any optimization.Aspheric A8 (1/mm^7) -6.17741E-19 -6.17741E-19 Print value. Not floated in any optimization.P-V residual profilometry fit (μm) 0.09 0.08 Profilometry residual error after fitting R and A4 of aspheric surface.

BINS-1011 - SN1 SN1 SN2Center Thickness (mm) 15.443 ± 0.0013 15.293 ± 0.0013Spherical surface radius (mm) 260.0162±8e-4 259.9919±8e-4 Value derived from DMI measurement from catseye to COCAspheric base radius (mm) 546.525 546.500 Value derived from profilometry and confirmed with ray trace analysisAspheric A4 (1/mm^3) -2.14761E-09 -2.15084E-09 Value derived from profilometry and confirmed with ray trace analysisAspheric A6 (1/mm^5) -1.04378E-14 -1.04378E-14 Print value. Not floated in any optimization.Aspheric A8 (1/mm^7) -1.36973E-19 -1.36973E-19 Print value. Not floated in any optimization.P-V residual profilometry fit (μm) 0.23 0.20 Profilometry residual error after fitting R and A4 of aspheric surface.

Table 1: Lens critical parameters

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3. Spherical Surface Roughness The following figure and table contain the surface roughness data for the spherical surfaces. The surface roughness images are appended to this document. Figures 1/2 shows the arrangement of measurements of surface roughness relative to the clear aperture and scribe line. All the spherical surfaces, with the exception of BINS1008 SN2 were measured in a pattern as shown on the left in figure 1. BINS1008 SN2 was measured in a pattern shown in figure 1 on the right. Surface roughness data was taken with a phase measuring microscope, over a 1.4mm diameter circular field.

Figure 1/2: Location of surface roughness measurements

Table 2 summarizes the surface roughness values. All values are in angstrom rms. BINS1001

SN1 BINS1001

SN2 BINS1008

SN1 BINS1008

SN2 BINS1011

SN1 BINS1011

SN2 Position 1 19.6 27.1 18.8 5.1 22.4 26.4 Position 2 18.8 27.8 23.9 4.6 20.1 27.0 Position 3 18.1 31.2 21.2 4.6 22.8 26.1 Position 4 17.5 24.7 22.6 5.3 21.3 26.0 Position 5 17.9 29.9 21.9 4.8 21.4 26.0 Average 18.4 28.1 21.7 4.9 21.6 26.3 Specification 30.0 30.0 30.0 30.0 30.0 30.0

Table 2: Surface Roughness Values for Spherical Surfaces

4. Spherical Surface Figure Error and Lens Element Transmitted WaveFront Error

The concave spherical surfaces (BINS1001/1011) were evaluated using a center of curvature test with a Fizeau interferometer. Data for the spherical surfaces is shown in table 3 below. For BINS1008 the

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spherical convex surfaces were pitch polished and verified to the power and irregularity requirements of the drawing. Profilometry verification of the radius of curvature was also performed. Images of the surface error is attached to this report as an appendix.

Surface Error

(λ rms HeNe) BINS1001 SN1 0.025 BINS1001 SN2 0.017 BINS1011 SN1 0.019 BINS1011 SN2 0.015

Table 3: Surface Error for Concave Spherical Surfaces Table 4 contains the 1-pass transmitted wavefront error for the null tests of the BINS optics.

Surface Error (λ rms HeNe)

BINS1001 SN1 0.038 BINS1001 SN2 0.030 BINS1008 SN1 0.019 BINS1008 SN2 0.039 BINS1011 SN1 0.026 BINS1011 SN2 0.028

Table 4: Transmitted Wavefront Error for Lens Elements

5. Slope Error Calculations and Results Calculation Method Tinsley calculated the RMS slope error based on transmitted wavefront data. The data pitch input into the slope calculation was selected at a density greater than the intrinsic interferometer measurement, so as not to under-sample any spatial wavelengths sampled by the interferometer. See table 5 for the data pitch of the measurements for all three of the optic types.

Part # # pixels across

CA in X # pixels across CA in Y

Pixel pitch in X (mm)

Pixel pitch in X (mm)

BINS-1001 655 655 0.524 0.524 BINS-1008 655 655 0.524 0.524 BINS-1011 655 655 0.524 0.524

Table 5: Data Density and Pixel Pitch in Buyoff TWFE data The RMS slope error is calculated using equation 1

∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎠⎞

⎜⎝⎛=

i dydz

dxdzsloperms

22

_ (1)

J. Daniel 6 7/16/06

where x and y are pixel pitch width and height, and z is wavefront height information.

Data Source and Manipulation: No frequency filtering, smoothing, windowing or clipping were performed on the data prior to calculation of RMS slope. RMS slope error is not calculated based on surface error measurements of the aspheric surface of the elements. No optical test was developed for this purpose. As such, the RMS slope is a combination of the slope error from the aspheric surface, the glass homogeneity, the spherical surface, and the test optics in the system. No systematic slope errors were removed from the measurement. The test optics are smooth surfaces, and contribute little to overall wavefront slope. Thus, the wavefront slope error reported is a worst case slope. The RMS slope errors of the six optics as measured are shown in table 6.

Part Description RMS WFE Slope (μrad)BINS1001 SN1 4.56BINS1001 SN2 3.00BINS1008 SN1 4.52BINS1008 SN2 4.85BINS1011 SN1 4.33BINS1011 SN2 4.52

Table 6: 1 pass TWFE As Measured Slope Error

The test optics are relatively smooth, compared to the TWFE data. The following methods were used to evaluate the contribution of the test optics to the composite slope error. For the transmission sphere, the reference surface was mapped. The data from the reference surface was then rotated to four positions (0, 90, 180 and 270 degrees) and averaged together to represent the contribution to a four position test. The data was then scaled in x and y to the size of the clear aperture on the asphere. The scaling is performed because while the trans sphere has a 100 mm aperture, the slope error of the aspheric element is scaled to the clear aperture of the aspheric surface. The portion of the transmission sphere reference surface used was thus scaled up in x/y to the size of the aspheric CA. This x/y scaled, four position average data slope error is shown in table 7. For the retro sphere, a similar procedure was used. The optic was tested at center of curvature in reflection. The data was rotated to four positions, averaged, and then scaled. In this case, the scaling scales down the size of the aperture, as the retro sphere CA is larger than the aspheric surface CA. For the CGH’s, the parts were tested in transmission with their 0-order. The data was again rotated/averaged/scaled. The data reported is the 1-pass TWFE of the CGH. As can be seen in table 7, the contributions from the transmission sphere, retro sphere, and CGH are relatively small. Although all the BINS parts used the same trans sphere and retro sphere, the three tests used three different apertures, so the rms slope contributions, from the trans sphere and retro sphere differ slightly.

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Part Description RMS WFE Slope (μrad)BINS1001 CGH 0.09BINS1001 Trans Sphere 0.21BINS1001 Retro Sphere 0.27BINS1008 CGH 0.62BINS1008 Trans Sphere 0.24BINS1008 Retro Sphere 0.30BINS1011 CGH 2.24BINS1011 Trans Sphere 0.19BINS1011 Retro Sphere 0.24

Table 7: 1 pass TWFE Contributions from Test Optics

6. Optical Axis Position, TIR of Cylinder, TIR of Spherical Surface Table 8 shows the optical axis position error with respect to the cylinder, and the cylinder TIR with respect to datum B. The derivation of these values is described in sections xx.

BINS1008-1 BINS1008-2 BINS1001-1 BINS1001-2 BINS1011-1 BINS1011-2 A Datum Centration to Cyl Position Error(mm) 0.022 0.025 0.008 0.004 0.011 0.023 Specification (mm) 0.025 0.025 0.025 0.025 0.025 0.025 Total TIR Cylinder to B (mm)- TIR Error(mm) 0.005 0.010 0.006 0.008 0.006 0.010 Specification (mm) 0.025 0.025 0.025 0.025 0.025 0.025 TIR Spherical Surface wrt Datum B (mm)- TIR Error(mm) 0.020 0.025 0.012 0.024 0.010 0.020 Specification (mm) 0.015 0.015 0.015 0.015 0.015 0.015

Table 8: Optical axis position error with respect to the cylinder, and the cylinder TIR with respect to datum B

7. Deviation of Aspheric Surfaces from Nominal Table 1 contains the deviation from nominal of the aspheric surface terms. The aspheric terms were calculated in the following manner. A grid of profilometry data was taken on the surface of interest. This data was azimuthally averaged into sag as a function of half diameter. Tinsley’s optimization software then determined the deviation of the measured sags from the theoretical sag data, and the values of vertex radius and A4 coefficient that best fit the sag data. Below are plots of the sag error associated with these deviations from nominal. Several curves are plotted. The yellow curves show the sag error deviation from nominal prescription aspheric sag. The

J. Daniel 8 7/16/06

blue curves show the sag error when aspheric base radius is floated to minimize rms sag error. The magenta curve shows sag error when aspheric base radius and the A4 deformation term are floated. In the sag plots, two plots are shown for the BINS1001 SN1 and SN2. The deviation in sag due to the base radius of curvature is large enough, that the deviation due to the A4 term is plotted separately on the right, to show greater detail. The data is the same as the curve on the left, with a smaller ordinate scale. For the BINS1008/1011 elements, the sag error is smaller, so all three curves are shown on one plot (yellow, blue and magenta).

BINS-1001 SN1 Sag Error

0.0E+002.0E-034.0E-036.0E-038.0E-031.0E-021.2E-021.4E-02

0.0 50.0 100.0 150.0Half Diameter (mm)

Sag

Erro

r (m

m) Nominal R/A4

Fit R

Fit R & A4

BINS-1001 SN1 Sag Error

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

3.5E-04

4.0E-04

0.0 50.0 100.0 150.0

Half Diameter (mm)

Sag

Erro

r (m

m)

Fit R

Fit R & A4

BINS-1008 SN2 Sag Errors

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

4.50E-03

5.00E-03

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0

Half Diameter (mm)

Z-H

eigh

t (m

m)

Nominal R and A4Fit RFit R & A4

BINS-1008 SN1 Profilometry Sag Error

-5.0E-04

0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

0.0 50.0 100.0 150.0

Half Diameter (mm)

Z-H

eigh

t (m

m)

Nominal R/A4

Fit R

Fit R & A4


-1.0E-04

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

0.0 50.0 100.0 150.0

Half Diameter (mm)

Z-H

eigh

t (m

m)

Fit R

Fit R & A4


-1.0E-03

1.0E-03

3.0E-03

5.0E-03

7.0E-03

9.0E-03

0.0 50.0 100.0 150.0

Half Diameter (mm)

Z-H

eigh

t (m

m)

Nominal R and A4

Fit R

Fit R & A4

J. Daniel 9 7/16/06

Figure 2: Sag Error Plots for BINS Aspheric Surfaces Sag tables containing nominal sag, as built sag, as built sag deviation from nominal, and as built sag deviation from the best fit R and A4 aspheric prescription are shown below. Sign convention follows Tinsley’s typical convention with convex surfaces (BINS1001 and BINS1011 aspheres) having a negative base radius and negative sags, and concave surfaces (BINS1008) having a positive base radius and positive sags. Specifically, for the BINS1001 aspheric surface, the radius and deformation terms are shown as positive on the drawing. For the data in figure 2 and in table 9 below, the signs of the radius and deformation terms are flipped. The same is done for BINS1008 and BINS1011. The Tinsley profilometry data analysis stream produces sag error data, not raw sag data. As such, the four data columns for each element are produced as follows. 1. The print sag column is an excel calculation of sag based on the drawing values. 2. The as built sag is the sum of the sag error data that our profilometry analysis produced, and the excel

calculated sag. The sag error data is plotted in figure 2. 3. The sag error is the difference between 1 and 2. 4. The sag error with R and A4 floating is the output of the Tinsley profilometry analysis.


0.0E+00

5.0E-041.0E-03

1.5E-03

2.0E-032.5E-03

3.0E-03

3.5E-034.0E-03

4.5E-03

0.0 50.0 100.0 150.0 200.0

Half Diameter (mm)

Z-H

eigh

t (m

m)



0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

3.0E-03

3.5E-03

4.0E-03

0.0 50.0 100.0 150.0 200.0

Half Diameter (mm)

Z-H

eigh

t (m

m)


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Half Diameter (mm)

Print Sag (mm)R= - 492.846058mma4= - 9.56848951e-10/mm^3a6= - 6.17861209e-15/mm^5a8= - 3.80667298e-19/mm^7

SN1 As Built Sag (mm)

SN1 As Built - Print Sag (mm)

SN1 Sag Error w/ R&A4 Floated (mm)R= - 492.9540 mma4= - 9.53020e-10/mm^3a6= - 6.17861209e-15/mm^5a8= - 3.80667298e-19/mm^7



SN2 Sag Error w/ R&A4 Floated (mm)R= - 493.0660 mma4= - 9.54457e-10/mm^3a6= - 6.17861209e-15/mm^5a8= - 3.80667298e-19/mm^7

0.000000E+00 0.0000000E+00 0.0000000E+00 0.0000E+00 6.0723E-05 0.0000000E+00 0.0000E+00 0.0000E+002.595349E+00 -6.8337025E-03 -6.8263060E-03 7.3964E-06 6.0870E-05 -6.8187788E-03 1.4924E-05 1.3330E-055.190698E+00 -2.7335900E-02 -2.7321020E-02 1.4879E-05 6.1018E-05 -2.7305928E-02 2.9971E-05 2.3595E-057.786047E+00 -6.1509861E-02 -6.1476066E-02 3.3795E-05 6.3964E-05 -6.1472782E-02 3.7078E-05 2.2724E-051.038140E+01 -1.0936104E-01 -1.0930038E-01 6.0660E-05 6.8730E-05 -1.0932257E-01 3.8470E-05 1.2933E-051.297675E+01 -1.7089708E-01 -1.7080875E-01 8.8326E-05 7.1796E-05 -1.7085591E-01 4.1170E-05 1.2285E-061.557209E+01 -2.4612780E-01 -2.4600650E-01 1.2131E-04 6.7844E-05 -2.4607740E-01 5.0408E-05 -7.1750E-061.816744E+01 -3.3506526E-01 -3.3491097E-01 1.5429E-04 6.3893E-05 -3.3500562E-01 5.9647E-05 -1.8840E-052.076279E+01 -4.3772370E-01 -4.3752792E-01 1.9578E-04 5.7174E-05 -4.3763628E-01 8.7425E-05 -1.5253E-052.335814E+01 -5.5411960E-01 -5.5387970E-01 2.3990E-04 4.9384E-05 -5.5399825E-01 1.2135E-04 -8.8365E-062.595349E+01 -6.8427169E-01 -6.8397813E-01 2.9357E-04 4.6013E-05 -6.8411903E-01 1.5266E-04 -8.3874E-062.854884E+01 -8.2820080E-01 -8.2783485E-01 3.6595E-04 5.1304E-05 -8.2802209E-01 1.7871E-04 -1.6599E-053.114418E+01 -9.8593032E-01 -9.8549199E-01 4.3833E-04 5.6594E-05 -9.8572556E-01 2.0476E-04 -2.8246E-053.373953E+01 -1.1574858E+00 -1.1569748E+00 5.1107E-04 4.8013E-05 -1.1572428E+00 2.4306E-04 -3.1119E-053.633488E+01 -1.3428953E+00 -1.3423113E+00 5.8395E-04 3.8359E-05 -1.3426127E+00 2.8258E-04 -3.6314E-053.893022E+01 -1.5421889E+00 -1.5415120E+00 6.7687E-04 4.0764E-05 -1.5418591E+00 3.2979E-04 -3.7411E-054.152560E+01 -1.7554016E+00 -1.7546121E+00 7.8943E-04 5.5014E-05 -1.7550174E+00 3.8421E-04 -3.4938E-054.412094E+01 -1.9825643E+00 -1.9816618E+00 9.0249E-04 6.8318E-05 -1.9821240E+00 4.4033E-04 -3.4491E-054.671629E+01 -2.2237167E+00 -2.2226980E+00 1.0188E-03 7.0141E-05 -2.2232021E+00 5.1460E-04 -1.9677E-054.931164E+01 -2.4788991E+00 -2.4777641E+00 1.1350E-03 7.1963E-05 -2.4783103E+00 5.8887E-04 -8.7200E-065.190698E+01 -2.7481543E+00 -2.7468833E+00 1.2710E-03 8.2263E-05 -2.7474881E+00 6.6615E-04 1.3166E-065.450233E+01 -3.0315277E+00 -3.0301109E+00 1.4168E-03 9.7080E-05 -3.0307827E+00 7.4504E-04 8.9489E-065.709768E+01 -3.3290677E+00 -3.3275039E+00 1.5638E-03 1.0856E-04 -3.3282410E+00 8.2675E-04 1.5310E-055.969302E+01 -3.6408254E+00 -3.6391122E+00 1.7132E-03 1.0982E-04 -3.6399092E+00 9.1614E-04 2.5151E-056.228837E+01 -3.9668548E+00 -3.9649922E+00 1.8626E-03 1.1108E-04 -3.9658493E+00 1.0055E-03 3.0710E-056.488372E+01 -4.3072131E+00 -4.3051879E+00 2.0251E-03 1.1059E-04 -4.3061308E+00 1.0823E-03 1.9243E-056.747909E+01 -4.6619640E+00 -4.6597737E+00 2.1902E-03 1.0990E-04 -4.6608071E+00 1.1569E-03 1.1537E-067.007443E+01 -5.0311641E+00 -5.0287997E+00 2.3644E-03 1.1044E-04 -5.0299177E+00 1.2464E-03 -6.6060E-067.266978E+01 -5.4148837E+00 -5.4123323E+00 2.5514E-03 1.1334E-04 -5.4135278E+00 1.3559E-03 9.3990E-077.526513E+01 -5.8131934E+00 -5.8104543E+00 2.7392E-03 1.1677E-04 -5.8117280E+00 1.4655E-03 3.7006E-067.786047E+01 -6.2261674E+00 -6.2232161E+00 2.9513E-03 1.2588E-04 -6.2245774E+00 1.5900E-03 1.6520E-058.045582E+01 -6.6538838E+00 -6.6507203E+00 3.1635E-03 1.3498E-04 -6.6521692E+00 1.7146E-03 2.4300E-058.305117E+01 -7.0964247E+00 -7.0930474E+00 3.3773E-03 1.3402E-04 -7.0945839E+00 1.8408E-03 2.8575E-058.564651E+01 -7.5538767E+00 -7.5502840E+00 3.5927E-03 1.2658E-04 -7.5519085E+00 1.9682E-03 2.8661E-058.824186E+01 -8.0263309E+00 -8.0225173E+00 3.8135E-03 1.2088E-04 -8.0242338E+00 2.0970E-03 2.4747E-059.083721E+01 -8.5138829E+00 -8.5098228E+00 4.0601E-03 1.2409E-04 -8.5116501E+00 2.2329E-03 2.2223E-059.343255E+01 -9.0166337E+00 -9.0123270E+00 4.3067E-03 1.2729E-04 -9.0142650E+00 2.3687E-03 1.3955E-059.602793E+01 -9.5346944E+00 -9.5301260E+00 4.5684E-03 1.2927E-04 -9.5321817E+00 2.5127E-03 8.0287E-069.862327E+01 -1.0068167E+01 -1.0063332E+01 4.8349E-03 1.3097E-04 -1.0065507E+01 2.6594E-03 -1.3786E-061.012186E+02 -1.0617173E+01 -1.0612065E+01 5.1081E-03 1.3147E-04 -1.0614355E+01 2.8179E-03 -5.1293E-061.038140E+02 -1.1181838E+01 -1.1176444E+01 5.3938E-03 1.2997E-04 -1.1178839E+01 2.9992E-03 7.5656E-061.064093E+02 -1.1762292E+01 -1.1756612E+01 5.6796E-03 1.2847E-04 -1.1759111E+01 3.1805E-03 1.3715E-051.090047E+02 -1.2358672E+01 -1.2352673E+01 5.9994E-03 1.3913E-04 -1.2355308E+01 3.3644E-03 1.5765E-051.116000E+02 -1.2971125E+01 -1.2964803E+01 6.3215E-03 1.5057E-04 -1.2967576E+01 3.5487E-03 1.1256E-051.141954E+02 -1.3599808E+01 -1.3593170E+01 6.6377E-03 1.4342E-04 -1.3596070E+01 3.7384E-03 5.1610E-061.167907E+02 -1.4244872E+01 -1.4237924E+01 6.9489E-03 1.1934E-04 -1.4240939E+01 3.9335E-03 -2.8979E-061.193861E+02 -1.4906494E+01 -1.4899231E+01 7.2629E-03 9.5487E-05 -1.4902363E+01 4.1308E-03 -1.6187E-051.219814E+02 -1.5584853E+01 -1.5577250E+01 7.6030E-03 7.4668E-05 -1.5580504E+01 4.3492E-03 -1.6007E-051.245768E+02 -1.6280140E+01 -1.6272196E+01 7.9432E-03 5.3849E-05 -1.6275572E+01 4.5676E-03 -2.3685E-051.271721E+02 -1.6992555E+01 -1.6984245E+01 8.3104E-03 4.1615E-05 -1.6987751E+01 4.8041E-03 -2.1341E-051.297675E+02 -1.7722312E+01 -1.7713622E+01 8.6895E-03 3.2743E-05 -1.7717263E+01 5.0491E-03 -1.8756E-051.323628E+02 -1.8469634E+01 -1.8460559E+01 9.0750E-03 2.2564E-05 -1.8464335E+01 5.2995E-03 -1.9262E-051.349582E+02 -1.9234759E+01 -1.9225279E+01 9.4802E-03 1.1484E-05 -1.9229194E+01 5.5653E-03 -1.3072E-051.375535E+02 -2.0017939E+01 -2.0008053E+01 9.8854E-03 4.0325E-07 -2.0012108E+01 5.8311E-03 -1.5821E-051.401489E+02 -2.0819445E+01 -2.0809108E+01 1.0337E-02 1.0057E-05 -2.0813321E+01 6.1245E-03 -1.9621E-071.427442E+02 -2.1639544E+01 -2.1628749E+01 1.0795E-02 2.2628E-05 -2.1633121E+01 6.4228E-03 1.0981E-051.453396E+02 -2.2478541E+01 -2.2467261E+01 1.1280E-02 4.7052E-05 -2.2471803E+01 6.7379E-03 2.9303E-051.479349E+02 -2.3336748E+01 -2.3324951E+01 1.1797E-02 8.7274E-05 -2.3329673E+01 7.0754E-03 6.0059E-051.505303E+02 -2.4214500E+01 -2.4202191E+01 1.2309E-02 1.2718E-04 -2.4207090E+01 7.4102E-03 7.8016E-05

SN1 SN2BINS1001

J. Daniel 11 7/16/06

Half Diameter (mm)

Print Sag (mm)R= 646.392194mma4= 3.70824810e-9/mm^3a6= 3.47213420e-14/mm^5a8= 6.17741230e-19/mm^7



SN1 Sag Error w/ R&A4 Floated (mm)R= 646.2724mma4= 3.70580e-9/mm^3a6= 3.47213420e-14/mm^5a8= 6.17741230e-19/mm^7



SN2 Sag Error w/ R&A4 Floated (mm)R= 646.1080mma4= 3.70268e-9/mm^3a6= 3.47213420e-14/mm^5a8= 6.17741230e-19/mm^7

0.000000E+00 0.0000000E+00 2.4672323E-05 2.4672E-05 2.4672E-05 0.0000000E+00 0.0000E+00 0.0000E+002.259166E+00 3.9480469E-03 3.9686931E-03 2.0646E-05 1.9914E-05 3.9633679E-03 1.5321E-05 1.0493E-054.518332E+00 1.5793488E-02 1.5810058E-02 1.6570E-05 1.3643E-05 1.5824436E-02 3.0948E-05 2.1102E-056.777500E+00 3.5540254E-02 3.5553014E-02 1.2760E-05 6.1772E-06 3.5586552E-02 4.6298E-05 2.9036E-059.036667E+00 6.3194868E-02 6.3204159E-02 9.2913E-06 -2.4051E-06 6.3255608E-02 6.0741E-05 2.8650E-051.129583E+01 9.8766438E-02 9.8772261E-02 5.8230E-06 -1.2440E-05 9.8841790E-02 7.5352E-05 2.8264E-051.355500E+01 1.4226683E-01 1.4227024E-01 3.4036E-06 -2.2872E-05 1.4236378E-01 9.6945E-05 3.0190E-051.581417E+01 1.9371045E-01 1.9371231E-01 1.8565E-06 -3.3871E-05 1.9383650E-01 1.2604E-04 3.4592E-051.807333E+01 2.5311434E-01 2.5311465E-01 3.0937E-07 -4.6301E-05 2.5326968E-01 1.5534E-04 3.8995E-052.033250E+01 3.2049835E-01 3.2050744E-01 9.0907E-06 -4.9822E-05 3.2069176E-01 1.9341E-04 4.5273E-052.259166E+01 3.9588509E-01 3.9590699E-01 2.1907E-05 -5.0717E-05 3.9612039E-01 2.3530E-04 5.2753E-052.485083E+01 4.7929975E-01 4.7933447E-01 3.4722E-05 -5.3007E-05 4.7957708E-01 2.7733E-04 6.0233E-052.711000E+01 5.7077062E-01 5.7082063E-01 5.0011E-05 -5.4205E-05 5.7108723E-01 3.1661E-04 5.6266E-052.936916E+01 6.7032745E-01 6.7039253E-01 6.5079E-05 -5.6989E-05 6.7068387E-01 3.5642E-04 5.1850E-053.162833E+01 7.7800604E-01 7.7808900E-01 8.2965E-05 -5.8303E-05 7.7840586E-01 3.9982E-04 4.9124E-053.388749E+01 8.9384061E-01 8.9395198E-01 1.1137E-04 -5.0429E-05 8.9429862E-01 4.5801E-04 5.3919E-053.614666E+01 1.0178734E+00 1.0180132E+00 1.3977E-04 -4.3866E-05 1.0183884E+00 5.1494E-04 5.8715E-053.840584E+01 1.1501458E+00 1.1503163E+00 1.7053E-04 -3.6238E-05 1.1507181E+00 5.7228E-04 5.8710E-054.066499E+01 1.2907019E+00 1.2909058E+00 2.0387E-04 -2.7291E-05 1.2913307E+00 6.2871E-04 5.2837E-054.292417E+01 1.4395938E+00 1.4398311E+00 2.3721E-04 -1.9586E-05 1.4402775E+00 6.8362E-04 4.6964E-054.518332E+01 1.5968703E+00 1.5971294E+00 2.5915E-04 -2.4502E-05 1.5976197E+00 7.4936E-04 4.2898E-054.744250E+01 1.7625903E+00 1.7628651E+00 2.7485E-04 -3.6842E-05 1.7634057E+00 8.1547E-04 4.0011E-054.970165E+01 1.9368088E+00 1.9370994E+00 2.9055E-04 -5.0344E-05 1.9376924E+00 8.8360E-04 3.7125E-055.196083E+01 2.1195923E+00 2.1199157E+00 3.2345E-04 -4.7788E-05 2.1205609E+00 9.6864E-04 4.4078E-055.421998E+01 2.3110023E+00 2.3113598E+00 3.5752E-04 -4.5157E-05 2.3120581E+00 1.0558E-03 5.2278E-055.647916E+01 2.5111130E+00 2.5115054E+00 3.9240E-04 -4.2786E-05 2.5122541E+00 1.1411E-03 5.9676E-055.873834E+01 2.7199955E+00 2.7204236E+00 4.2810E-04 -4.0638E-05 2.7212252E+00 1.2297E-03 6.4398E-056.099749E+01 2.9377248E+00 2.9381886E+00 4.6379E-04 -3.9492E-05 2.9390480E+00 1.3233E-03 6.9121E-056.325667E+01 3.1643871E+00 3.1648946E+00 5.0742E-04 -3.1377E-05 3.1658000E+00 1.4128E-03 7.2113E-056.551582E+01 3.4000631E+00 3.4006251E+00 5.6196E-04 -1.3276E-05 3.4015730E+00 1.5098E-03 7.3246E-056.777500E+01 3.6448481E+00 3.6454646E+00 6.1651E-04 3.9354E-06 3.6464497E+00 1.6016E-03 7.4379E-057.003418E+01 3.8988340E+00 3.8994923E+00 6.5834E-04 7.5860E-06 3.9005306E+00 1.6966E-03 7.5096E-057.229333E+01 4.1621170E+00 4.1628087E+00 6.9165E-04 1.9067E-06 4.1639171E+00 1.8001E-03 7.6155E-057.455251E+01 4.4348072E+00 4.4355322E+00 7.2496E-04 -4.5378E-06 4.4367051E+00 1.8979E-03 7.7214E-057.681166E+01 4.7170077E+00 4.7177823E+00 7.7461E-04 4.6418E-06 4.7190110E+00 2.0033E-03 7.8436E-057.907084E+01 5.0088393E+00 5.0096654E+00 8.2610E-04 1.4985E-05 5.0109462E+00 2.1069E-03 8.0325E-058.132999E+01 5.3104154E+00 5.3112919E+00 8.7642E-04 2.3522E-05 5.3126316E+00 2.2162E-03 8.0455E-058.358916E+01 5.6218686E+00 5.6227764E+00 9.0778E-04 1.2524E-05 5.6241803E+00 2.3116E-03 6.9747E-058.584832E+01 5.9433236E+00 5.9442628E+00 9.3914E-04 9.9722E-07 5.9457345E+00 2.4108E-03 5.9039E-058.810749E+01 6.2749255E+00 6.2759012E+00 9.7566E-04 -5.8442E-06 6.2774398E+00 2.5143E-03 5.1203E-059.036667E+01 6.6168154E+00 6.6178346E+00 1.0193E-03 -6.0213E-06 6.6194393E+00 2.6240E-03 5.1075E-059.262582E+01 6.9691403E+00 6.9702032E+00 1.0629E-03 -6.5717E-06 6.9718820E+00 2.7417E-03 5.0948E-059.488500E+01 7.3320667E+00 7.3331758E+00 1.1090E-03 -4.9468E-06 7.3349154E+00 2.8487E-03 4.6376E-059.714415E+01 7.7057523E+00 7.7069072E+00 1.1548E-03 -3.8682E-06 7.7087112E+00 2.9589E-03 3.9822E-059.940333E+01 8.0903791E+00 8.0915798E+00 1.2007E-03 -2.9949E-06 8.0934442E+00 3.0650E-03 3.3269E-051.016625E+02 8.4861202E+00 8.4873659E+00 1.2457E-03 -3.0473E-06 8.4893133E+00 3.1930E-03 3.8392E-051.039217E+02 8.8931748E+00 8.8944641E+00 1.2893E-03 -4.6593E-06 8.8964909E+00 3.3160E-03 4.6961E-051.061808E+02 9.3117330E+00 9.3130676E+00 1.3346E-03 -4.5878E-06 9.3151753E+00 3.4422E-03 5.3881E-051.084400E+02 9.7420127E+00 9.7433976E+00 1.3848E-03 5.0688E-07 9.7455733E+00 3.5606E-03 5.2305E-051.106991E+02 1.0184223E+01 1.0185658E+01 1.4351E-03 5.7046E-06 1.0187902E+01 3.6792E-03 5.0728E-051.129583E+02 1.0638601E+01 1.0640083E+01 1.4818E-03 7.5547E-06 1.0642394E+01 3.7926E-03 4.3766E-051.152175E+02 1.1105383E+01 1.1106899E+01 1.5158E-03 -3.1459E-06 1.1109275E+01 3.8915E-03 2.7772E-051.174767E+02 1.1584813E+01 1.1586363E+01 1.5498E-03 -1.3543E-05 1.1588809E+01 3.9959E-03 1.1778E-051.197358E+02 1.2077165E+01 1.2078754E+01 1.5897E-03 -1.7563E-05 1.2081269E+01 4.1039E-03 5.7136E-061.219950E+02 1.2582701E+01 1.2584333E+01 1.6314E-03 -1.9468E-05 1.2586935E+01 4.2335E-03 1.0500E-051.242542E+02 1.3101721E+01 1.3103394E+01 1.6730E-03 -2.0860E-05 1.3106073E+01 4.3520E-03 1.5287E-051.265133E+02 1.3634521E+01 1.3636229E+01 1.7079E-03 -2.8409E-05 1.3638996E+01 4.4744E-03 2.6384E-051.287725E+02 1.4181409E+01 1.4183148E+01 1.7388E-03 -3.9279E-05 1.4186022E+01 4.6123E-03 4.1129E-051.310317E+02 1.4742728E+01 1.4744499E+01 1.7705E-03 -4.8670E-05 1.4747477E+01 4.7483E-03 6.6858E-05

BINS1008SN1 SN2

J. Daniel 12 7/16/06

The BINS1011 profilometry data was gridded out onto a slightly different ½ diameter pitch for SN1 vs. SN2, thus two tables are shown for these elements.

Half Diameter (mm)

Print Sag (mm)R= -546.331433mma4= 2.15623600e-9/mm^3a6= 1.04377570e-14/mm^5a8= 1.36972930e-19/mm^7



SN1 Sag Error w/ R&A4 Floated (mm)R= -546.525mma4= 2.14761e-9/mm^3a6= 1.04377570e-14/mm^5a8= 1.36972930e-19/mm^7

0.000000E+00 0.0000000E+00 1.0878985E-05 1.0879E-05 1.7768E-042.928422E+00 -7.8482973E-03 -7.8428186E-03 5.4787E-06 1.6810E-045.856841E+00 -3.1391935E-02 -3.1391935E-02 0.0000E+00 1.6268E-048.785263E+00 -7.0627272E-02 -7.0606376E-02 2.0897E-05 1.5966E-041.171368E+01 -1.2554815E-01 -1.2550188E-01 4.6272E-05 1.7467E-041.464210E+01 -1.9614589E-01 -1.9604611E-01 9.9779E-05 2.0680E-041.757053E+01 -2.8240950E-01 -2.8224470E-01 1.6480E-04 2.2169E-042.049895E+01 -3.8432532E-01 -3.8412487E-01 2.0045E-04 2.0638E-042.342737E+01 -5.0187721E-01 -5.0166347E-01 2.1374E-04 1.9237E-042.635578E+01 -6.3504575E-01 -6.3480658E-01 2.3917E-04 1.8293E-042.928422E+01 -7.8381211E-01 -7.8353080E-01 2.8130E-04 1.7331E-043.221264E+01 -9.4814935E-01 -9.4782338E-01 3.2597E-04 1.6375E-043.514105E+01 -1.1280321E+00 -1.1276539E+00 3.7820E-04 1.5419E-043.806947E+01 -1.3234311E+00 -1.3230007E+00 4.3033E-04 1.3411E-044.099789E+01 -1.5343141E+00 -1.5338337E+00 4.8042E-04 1.1294E-044.392633E+01 -1.7606484E+00 -1.7601179E+00 5.3051E-04 1.0687E-044.685475E+01 -2.0023921E+00 -2.0017842E+00 6.0792E-04 1.0511E-044.978316E+01 -2.2595063E+00 -2.2588203E+00 6.8600E-04 9.8732E-055.271158E+01 -2.5319471E+00 -2.5311828E+00 7.6430E-04 8.9921E-055.564000E+01 -2.8196674E+00 -2.8188246E+00 8.4289E-04 8.7168E-055.856841E+01 -3.1226171E+00 -3.1216827E+00 9.3441E-04 9.0979E-056.149685E+01 -3.4407451E+00 -3.4397131E+00 1.0320E-03 9.3087E-056.442527E+01 -3.7739888E+00 -3.7728593E+00 1.1296E-03 9.1546E-056.735369E+01 -4.1222903E+00 -4.1210633E+00 1.2270E-03 9.3492E-057.028210E+01 -4.4855849E+00 -4.4842520E+00 1.3329E-03 1.0998E-047.321052E+01 -4.8638043E+00 -4.8623523E+00 1.4520E-03 1.2613E-047.613896E+01 -5.2568795E+00 -5.2553093E+00 1.5701E-03 1.3705E-047.906738E+01 -5.6647269E+00 -5.6630411E+00 1.6858E-03 1.4798E-048.199580E+01 -6.0872689E+00 -6.0854682E+00 1.8008E-03 1.5246E-048.492421E+01 -6.5244198E+00 -6.5225100E+00 1.9098E-03 1.5628E-048.785263E+01 -6.9760888E+00 -6.9740700E+00 2.0188E-03 1.5494E-049.078105E+01 -7.4421805E+00 -7.4400605E+00 2.1200E-03 1.5161E-049.370946E+01 -7.9225939E+00 -7.9203735E+00 2.2205E-03 1.4879E-049.663791E+01 -8.4172269E+00 -8.4149078E+00 2.3190E-03 1.4648E-049.956632E+01 -8.9259584E+00 -8.9235411E+00 2.4172E-03 1.4293E-041.024947E+02 -9.4486742E+00 -9.4461641E+00 2.5101E-03 1.3790E-041.054232E+02 -9.9852492E+00 -9.9826490E+00 2.6002E-03 1.3857E-041.083516E+02 -1.0535552E+01 -1.0532856E+01 2.6958E-03 1.5170E-041.112800E+02 -1.1099447E+01 -1.1096651E+01 2.7964E-03 1.6239E-041.142084E+02 -1.1676780E+01 -1.1673892E+01 2.8881E-03 1.6105E-041.171368E+02 -1.2267400E+01 -1.2264435E+01 2.9643E-03 1.5980E-041.200653E+02 -1.2871143E+01 -1.2868106E+01 3.0380E-03 1.5834E-041.229937E+02 -1.3487839E+01 -1.3484738E+01 3.1015E-03 1.5684E-041.259221E+02 -1.4117306E+01 -1.4114140E+01 3.1654E-03 1.7114E-041.288505E+02 -1.4759351E+01 -1.4756119E+01 3.2322E-03 1.8794E-041.317790E+02 -1.5413781E+01 -1.5410482E+01 3.2991E-03 2.0353E-041.347074E+02 -1.6080369E+01 -1.6077021E+01 3.3482E-03 2.1864E-041.376358E+02 -1.6758898E+01 -1.6755503E+01 3.3956E-03 2.2596E-041.405642E+02 -1.7449131E+01 -1.7445714E+01 3.4167E-03 2.2735E-041.434926E+02 -1.8150818E+01 -1.8147388E+01 3.4297E-03 2.2123E-041.464210E+02 -1.8863695E+01 -1.8860278E+01 3.4172E-03 2.0459E-041.493495E+02 -1.9587491E+01 -1.9584103E+01 3.3887E-03 1.8922E-041.522779E+02 -2.0321901E+01 -2.0318551E+01 3.3498E-03 1.7697E-041.552063E+02 -2.1066621E+01 -2.1063322E+01 3.2990E-03 1.6555E-041.581347E+02 -2.1821325E+01 -2.1818085E+01 3.2409E-03 1.5985E-041.610632E+02 -2.2585670E+01 -2.2582503E+01 3.1667E-03 1.5416E-041.639916E+02 -2.3359298E+01 -2.3356222E+01 3.0760E-03 8.5097E-051.669200E+02 -2.4141814E+01 -2.4138910E+01 2.9032E-03 1.3955E-051.698484E+02 -2.4932820E+01 -2.4930088E+01 2.7316E-03 2.2791E-04

BINS1011 SN1

J. Daniel 13 7/16/06

Half Diameter (mm)

Print Sag (mm)R= -546.331433mma4= 2.15623600e-9/mm^3a6= 1.04377570e-14/mm^5a8= 1.36972930e-19/mm^7



SN2 Sag Error w/ R&A4 Floated (mm)R= -546.500mma4= 2.15084e-9/mm^3a6= 1.04377570e-14/mm^5a8= 1.36972930e-19/mm^7

0.000000E+00 0.0000E+00 0.0000000E+00 0.0000E+00 9.3735E-052.928074E+00 -7.8464E-03 -7.8282028E-03 1.8229E-05 1.0686E-045.856150E+00 -3.1385E-02 -3.1347981E-02 3.6549E-05 1.0250E-048.784227E+00 -7.0611E-02 -7.0569748E-02 4.0865E-05 8.8883E-051.171230E+01 -1.2552E-01 -1.2547570E-01 4.2789E-05 8.8377E-051.464038E+01 -1.9610E-01 -1.9602941E-01 7.0220E-05 1.0062E-041.756845E+01 -2.8234E-01 -2.8223459E-01 1.0824E-04 1.1135E-042.049653E+01 -3.8423E-01 -3.8408509E-01 1.4953E-04 1.1953E-042.342460E+01 -5.0176E-01 -5.0156519E-01 1.9351E-04 1.2883E-042.635268E+01 -6.3490E-01 -6.3465298E-01 2.4361E-04 1.4198E-042.928076E+01 -7.8363E-01 -7.8332515E-01 3.0229E-04 1.5400E-043.220883E+01 -9.4793E-01 -9.4756661E-01 3.5882E-04 1.4966E-043.513691E+01 -1.1278E+00 -1.1273575E+00 4.0938E-04 1.4532E-043.806497E+01 -1.3231E+00 -1.3226586E+00 4.6064E-04 1.3777E-044.099306E+01 -1.5340E+00 -1.5334373E+00 5.1656E-04 1.2987E-044.392112E+01 -1.7602E+00 -1.7596598E+00 5.7248E-04 1.1949E-044.684921E+01 -2.0019E+00 -2.0012870E+00 6.3346E-04 1.0848E-044.977727E+01 -2.2590E+00 -2.2582788E+00 6.9466E-04 1.0810E-045.270536E+01 -2.5314E+00 -2.5305756E+00 7.7632E-04 1.1415E-045.563342E+01 -2.8190E+00 -2.8181416E+00 8.6236E-04 1.1955E-045.856150E+01 -3.1219E+00 -3.1209322E+00 9.5230E-04 1.2432E-046.148959E+01 -3.4399E+00 -3.4388930E+00 1.0442E-03 1.2499E-046.441765E+01 -3.7731E+00 -3.7719694E+00 1.1328E-03 1.1729E-046.734574E+01 -4.1213E+00 -4.1201059E+00 1.2185E-03 1.1012E-047.027380E+01 -4.4845E+00 -4.4832260E+00 1.3074E-03 1.0505E-047.320189E+01 -4.8627E+00 -4.8612659E+00 1.4012E-03 9.9976E-057.612995E+01 -5.2556E+00 -5.2541497E+00 1.4967E-03 9.8112E-057.905803E+01 -5.6634E+00 -5.6618035E+00 1.5983E-03 9.6249E-058.198609E+01 -6.0858E+00 -6.0841434E+00 1.7013E-03 1.0538E-048.491418E+01 -6.5229E+00 -6.5210785E+00 1.8187E-03 1.1576E-048.784224E+01 -6.9745E+00 -6.9725250E+00 1.9360E-03 1.1836E-049.077033E+01 -7.4404E+00 -7.4384026E+00 2.0458E-03 1.1829E-049.369842E+01 -7.9208E+00 -7.9185994E+00 2.1551E-03 1.1866E-049.662648E+01 -8.4153E+00 -8.4130027E+00 2.2661E-03 1.1936E-049.955456E+01 -8.9239E+00 -8.9215099E+00 2.3775E-03 1.1708E-041.024826E+02 -9.4465E+00 -9.4439984E+00 2.4845E-03 1.1102E-041.054107E+02 -9.9829E+00 -9.9803504E+00 2.5892E-03 1.0909E-041.083388E+02 -1.0533E+01 -1.0530416E+01 2.7002E-03 1.1687E-041.112669E+02 -1.1097E+01 -1.1094066E+01 2.8174E-03 1.2316E-041.141949E+02 -1.1674E+01 -1.1671155E+01 2.9303E-03 1.2131E-041.171230E+02 -1.2265E+01 -1.2261542E+01 3.0353E-03 1.1940E-041.200511E+02 -1.2868E+01 -1.2865046E+01 3.1385E-03 1.1327E-041.229792E+02 -1.3485E+01 -1.3481513E+01 3.2350E-03 1.0717E-041.259072E+02 -1.4114E+01 -1.4110743E+01 3.3316E-03 1.0365E-041.288353E+02 -1.4756E+01 -1.4752558E+01 3.4254E-03 1.0040E-041.317634E+02 -1.5410E+01 -1.5406750E+01 3.5191E-03 1.1362E-041.346915E+02 -1.6077E+01 -1.6073084E+01 3.6275E-03 1.3417E-041.376195E+02 -1.6755E+01 -1.6751361E+01 3.7378E-03 1.6190E-041.405476E+02 -1.7445E+01 -1.7441332E+01 3.8511E-03 1.9542E-041.434757E+02 -1.8147E+01 -1.8142760E+01 3.9654E-03 2.0731E-041.464037E+02 -1.8859E+01 -1.8855411E+01 4.0409E-03 1.8747E-041.493318E+02 -1.9583E+01 -1.9579005E+01 4.0911E-03 1.6957E-041.522599E+02 -2.0317E+01 -2.0313214E+01 4.1390E-03 1.5697E-041.551880E+02 -2.1062E+01 -2.1057742E+01 4.1840E-03 1.4406E-041.581160E+02 -2.1816E+01 -2.1812252E+01 4.2241E-03 1.2604E-041.610441E+02 -2.2581E+01 -2.2576421E+01 4.2527E-03 1.0803E-041.639722E+02 -2.3354E+01 -2.3349873E+01 4.2756E-03 5.9551E-051.669003E+02 -2.4137E+01 -2.4132240E+01 4.2705E-03 9.9684E-061.698284E+02 -2.4927E+01 -2.4923107E+01 4.2653E-03 2.1515E-04

BINS1011 SN2SN2

Table 9: Sag tables for the BINOSPEC aspheric surfaces

J. Daniel 14 7/16/06

8. Comparison of Profilometry Derived Aspheric Best Fit Prescription to Ray Trace Results

To confirm the values of aspheric R and A4 terms that were measured using profilometry, these terms along with other critical element parameters, such as spherical radius and center thickness were loaded into the null test ray trace models. The BINS1001 null test ray trace layout is shown in figure 3. The basic figure is from Diffraction International’s holographic null test report. In this null test, the hologram generates an aspheric wavefront that propagates through the BINS1001 element. BINS1001 converts this wavefront into a spherical wavefront that retro reflects off the retro sphere, and returns back through the system into the interferometer, on which the transmission sphere is mounted.

v Figure 3: BINS1001 null test ray trace model

As built values from table 1 were loaded into the ray trace model. The residual error for the 2-pass ray trace model is shown in figure 4. The 1-pass WFE residual is only 0.018λ rms HeNe. To further confirm that the trace model is confirming that the as-built lens shape generates a null, the value of the deviation in A4 shape from nominal can be compared to the amount of shape ray trace. The deviation in sag of the refocused A4 shape is 287 nm P-V. The amount of shape in the aspheric surface that would cause the P-V null test 1-pass WFE residual is 30*1.55 nm P-V (1.55 in the index of the glass @ HeNe). This comparison shows that despite loading a different spherical aberration term (A4) into the ray trace model, the other changes (CT, surface radii) cause the modified spherical aberration value to be nulled.

Retro sphere

BINS1001 element

Hologram

Transmission sphere

Catseye

J. Daniel 15 7/16/06

Figure 4: BINS1001 SN1 as built residual 2-pass WFE

Figures 5, 6, and 7 show the ray trace result for the BINS1001 SN2 part, as well as the ray trace result for BINS1008 SN1 and SN2. These results also demonstrate the agreement between the profilometry results and the ray trace model loaded with lens as builts.


J. Daniel 16 7/16/06



The ray trace model for BINS1011 initially showed disagreement between the profilometry results and the ray trace results. The as built ray trace results showed approximately a wave of spherical aberration (2-pass P-V WFE) as shown in figures 7 and 8.

Figure 7/8: BINS1011 SN1/SN2 as built residual 2-pass WFE

J. Daniel 17 7/16/06

The source of this error was not understood until the BINS1011 element was tested @ 20C, at which temperature the ray trace was modeled. It was found that while at 24C, the BINS1011 exhibited an in-spec wavefront error, at 20C, the same lens element exhibited spherical aberration that agreed with the ray trace prediction shown in Figure 7/8. Figure 9 is an actual test result WFE plot for BINS1011 SN1. The 0.50λ P-V spherical aberration seen in figure 9 agrees well with the expected 0.60λ P-V error predicted by the as built ray trace (figure 7&8).

Figure 9: BINS1011 SN1 tested 1-pass WFE data from test @ 20C

9. Additional Information On Drawing Note Callouts The following indices contain additional information expanding on the drawing notes. For example, the descriptions in “2)” below refer to note 2 on the BINS drawings. 2) Spherical surfaces were conventionally pitch polished, and in some cases, subsequently processed through Tinsley's small tool polishing department (CCOS). These will be discussed further in notes 6, 7, and 8. As requested the cylinder/girdle and face flat of the lenses were ground to a 400 grit finish. The Collimator 8 lenses were non-conformant to this specification due to having the face flat inspection polished. 3) All reflected wavefront and transmitted wavefront optical tests were performed by Tinsley utilizing the reference wavelength of 6328 Angstroms with an ADE Phase Shift Minifiz interferometer. 4) Tinsley QA measured the final center thicknesses. Stated center thicknesses were measured to an accuracy of ±0.0013 mm.

BINS-1001 Center Thickness Nominal CT (mm) 15.242 ± 0.2 Serial Number 1 (mm) 15.364 ± 0.0013 Serial Number 2 (mm) 15.347 ± 0.0013

BINS-1008 Center Thickness Nominal CT (mm) 16.834 ± 0.2 Serial Number 1 (mm) 16.787 ± 0.0013 Serial Number 2 (mm) 16.871 ± 0.0013

J. Daniel 18 7/16/06

BINS-1011 Center Thickness

Nominal CT (mm) 15.241 ± 0.2 Serial Number 1 (mm) 15.443 ± 0.0013 Serial Number 2 (mm) 15.293 ± 0.0013

Table 10: As built CT’s 5) Scratch/Dig: Pass/Conform. 6) Surface Finish: Spherical surface finish to better than 30 Angstroms RMS was verified using a white light interferometer (ADE Phase Shift Technologies Micro-exam) fitted with 1024 by 1024 pixel CCD camera. All measurements were completed using subapertures measuring 1.4 mm square. A 10X objective was used to measure spatial periods from 0.12 mm to 0.01 mm's. The systematic error of the instrument background (inherent errors) was calibrated by measuring five independent subapertures, and then calculating the average of these measurements. Subsequent measurements were then made at the outlined locations below and the resulting Rq value reported was obtained by subtracting the background file from the measurement. Values are listed in section 3, and images are appended to this report.

10. Radius of Curvature Measurements 7) Radius of Curvature of the Spherical Surface: A test plate was used during the conventional polishing phase of the finishing process for both BINS-1008 lenses. A test plate was not used during the conventional polishing step of the finishing process of BINS-1001 and BINS-1011. During the conventional polishing phase of the finishing process the radius and surface figure were controlled using a distance measuring interferometer (DMI) in conjunction with an ADE Phase Shift Minifiz interferometer fitted with an F/0.65 transmission sphere. The DMI was used to measure the radius of curvature while the Minifiz interferometer measured the surface figure error. The distance measuring interferometer station gathers data on air temperature and humidity, to allow the index of the air to be accurately known.

Concave/Spherical Wavefront Test Layout for BINS-1001 and BINS-1011:

Figure 10: Setup for measuring radius of curvature

• Controlled test Temperature = 24 °C +/- 2 °C. Final Optical test completed at 23 °C.

J. Daniel 19 7/16/06

• Lens was mounted on a stable 5-axis mount with the concave surface facing the interferometer. • The 5-axis mount is calibrated to move away from the interferometer on the optical axis to within 0.2 milli-

radians. • Wavefront error was measured using a Fizeau interferometer. • Distance was measured using a Distance Measuring Interferometer (DMI).

Radius of Curvature Test Procedure for the Spherical Surface:

• Translate the lens to the Cat’s Eye of the f/0.65 diverger/transmission sphere. • Adjust x/y-translation of the Lens to center the Lens relative to the source spot. • Move the lens to the Radius of Curvature position. Adjust rx/ry of the lens until the radius of curvature

falls onto the source spot. • Iterate between the previous two steps until motion along z-axis does not require adjustment at the cat eye

or ROC position. • Zero the DMI. • Translate the lens to the radius of curvature. • Phase the Minifiz interferometer to capture an image of the wavefront error. Record the focus Zernike term

and DMI reading. • Move lens to Cat’s Eye position of the f/0.65 diverger. • Phase the interferometer to obtain a surface map. Record the focus Zernike term and DMI reading. • Repeat the previous four steps until a good distribution is obtained. • Plot Focus vs. DMI reading for each phase position. Assuming a low order linear fit calculate where Focus

= 0 for each position. The radius of curvature of the surface is then given by the difference in the Z value at each of these positions.

11. Error Analysis Associated with the DMI Measurement for Radius of Curvature of the Spherical Surface

Introduction: This discussion outlines measurement errors in the spherical testing of SAO Binospec Collimator Lens 1 and Camera Lens 1. The Zygo11 Distance Measuring Interferometer (abbreviated DMI) works on the general principle of an interferometer. Using the interference pattern between the reference and return beam of a He-Ne laser it measures relative motions of a target. Zygo suggests three possible uncertainties which will cause DMI measurement error:

• Environment Errors. • Geometry Errors. • Instrument Errors.

Outlined is a general analysis of these measurement errors. Assuming linear independence of the error sources, the RSS value for the measurement uncertainty is: ΔDistance = √ {(ΔDE)2+(ΔDG) 2+(ΔDI) 2} Environment Errors:

1 All references to Zygo are references to the Zygo instruction manual and enclosed study, “A Primer on Displacement Measuring Interferometers”.

J. Daniel 20 7/16/06

Environment errors cause major changes in the index of refraction of the media in which the measurements are taking place. This can cause serious losses in measurement accuracy. The largest factors in this error are temperature, humidity, and pressure. The Zygo interferometer interface uses a calibrated Davis Perception II weather station to measure these parameters and correct for the wavelength. The general form for this measurement is:

DE = m * λ (1.1) where m is the number of relative clicks between the two measurement positions and λ = λo/n (n being the index of refraction of the media and λo = 632.8 nm, the wavelength of the He-Ne laser in vacuum) The uncertainty is then given as:

ΔDE = m *Δ λ (1.2)

and Δ λ = - λo * Δ n / n2 where Δ denotes uncertainties. Simplifying, the measurement uncertainty in the distance measurement (D) becomes: ΔDE = D * Δ n / n . (1.3) with D being the distance measured. Without derivation, the Edlen Equation for the relationship of the index of refraction on temperature, pressure and humidity 1 is:

n = 1 + k1 * P / (T+273) – k2* H * (T2+160) (1.4) Where P is the pressure given in kPa , H is the relative humidity as a percentile, and T is the temperature in oC. The constants k1 and k2 are 7.86e-4 oC /kPa and 1.5e-11 / oC respectively. This form is valid only for a He-Ne laser in an environment range of

0 < To < 30 oC 0 < Ho < 100 % 520 < Po = 120 kPa

and is stated to be approximate to within 1.5e-7 1. Assuming linear independence of the three parameters, equation 1.1 gives the uncertainty relationships as:

Δnp = k1/(To+273) * ΔP Δnh = - k2 * (To

2+160) * ΔH (1.5)

ΔnT = (-k1 * Po / (To+273) – 2 * k2 * Ho * To)* ΔT

2 Stone, Jack A. and Zimmerman, Jay H. , “Index of Refraction of Air” , Engineering Metrology Toolbox , http://emtoolbox.nist.gov/Wavelength/Documentation.asp .

J. Daniel 21 7/16/06

where the values To , Ho , Po are the normal operating environment parameters and the Δ indicate the uncertainties in each measurement. The total uncertainty in the index of refraction is then:

Δn =√ {(Δnp)2+( Δnh) 2+( ΔnT) 2} (1.6) The environment measurements in the optics lab give the following operating parameters:

To = 21 oC ΔT = 0.1 oC Ho = 60 % ΔH = 0.1 % Po = 102.100 kPa ΔP = 0.013 kPa

The calculated index of refraction is then:

n =1.000273 Δn = 2.8E-06 And, from equation 1.3, the measurement uncertainties for BINS1001 and BINS1011 respectively are then:

ΔDE = 0.00059 mm ΔDE = 0.00074 mm

Geometry Errors: Geometry errors are generated by a displacement of the target surface from the line of the DMI beam (referred to as Cosine Error). The restriction placed on this misalignment by Zygo is 50% the beam waist of the returning interferometer beam. After this point, the interferometer will not read consistently. The approximated equation of the beam waist 33 is: w(z) = (λ * z) / (π * wo) * [1+0.5*( (π * wo

2)/ (λ * z)) 2] where wo is the beam waist leaving the interferometer and z is the distance the beam travels to get back to the interferometer. The accepted value for a He-Ne laser is wo = 0.7 mm. In the alignment process, the rail travel length is z = 2300 mm. This gives a returning beam waist of w = 1.5 mm. From simple derivation, the approximated maximum angle error accepted by the DMI (in this case) is then:

α = w / (4*z) = 0.328 milli-radians The uncertainty in measurement is then given by the approximated relationship:

ΔDG = D * α2 / 2 The resulting uncertainties for BINS1001 and BINS1011 respectively are:

ΔDG = 0.000011 mm

3 “Gaussian Beam Propagation–Beam Waist and Divergence”, Melles Griot Optics Guide, http://optics.mellesgriot.com/opguide/gb_2_1.htm .

J. Daniel 22 7/16/06

ΔDG = 0.000014 mm Instrumentation Errors Zygo suggests the instrumentation measurement errors are generated by the DMI computer’s ability to count the number of ticks generated through movement of the target surface and the ability to measure the reference points in the measurement. It is assumed that the ability to measure the ticks by the computer is negligible in the radius measurement. This leaves the measurement uncertainty of the generated by instrumentation errors to the ability of the user to determine the reference points of the measurement. The first error generated is called Abbe Offset (ΔA). This error is generated by the tilt generated in the surface from motion between the two measurement points (similar to cosine error). Prior to measurement, the part is tilted in its fixture such that motion between the two reference points of the measurement generates < 10 λ of tilt in the wavefront. From simple analysis, this shows that the Abbe offset is negligible. The second error is the user’s ability to measure the two reference points of the sphere under test. For this measurement the wavefronts of two points are measured with a Fizeau interferometer in conjunction with the DMI in continuous read mode. The focus error is then plotted as a function of z-translation to determine the points of zero focus. Example graphs depicting the location of both of these reference points are below.

Radius of Curvature y = 5369.2x - 0.9973R2 = 0.9646

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

-0.00040 -0.00020 0.00000 0.00020 0.00040 0.00060 0.00080 0.00100

Z Position (in)

Focu

s Ze

rnik

ie (w

v)

Cat's Eye y = 5938.8x + 48924R2 = 0.9607

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

-8.23840 -8.23820 -8.23800 -8.23780 -8.23760 -8.23740

Z Position (in)

Focu

s Ze

rnik

ie (w

v)

Figure 11/12: Fitting of zero focus cross over point for measurement of radius of curvature

The Cat’s Eye position is the point at which the interferometer is in retro-reflection with the surface of the optic. The radius of curvature occurs when the source is in auto-collimation with the surface. Assuming the relationship between focus and z-position near the two points is linear; the above linear fit allows direct calculation of the zero position and the uncertainty of the measurement at the two reference points (ΔU). Using the example above, the uncertainty in the zero position is 0.0003mm. The final error source comes from the ability to measure the retro-reflection position with surface defects (ΔPV). This error source can be seen, as a maximum, to be the Peak to Valley specification on the part. This is given as λ/6. The table below shows the resulting uncertainty in the final measurement of the surface in both cases.

ΔU = 0.0003 mm

J. Daniel 23 7/16/06

ΔA = 0.00000 mm ΔPV = 0.000004 mm ΔDI = 0.000011 mm

Conclusion: Below are the resulting error trees containing the DMI measurement uncertainties for each BINS-1001 and BINS-1011 radius measurements:

Part- BINS1001

Radius(mm)- 2.09E+02

Part Dia(mm)- 3.05E+02 ΔD(mm)

6.64E-04

ΔDG(mm) ΔDI(mm) ΔDE(mm) 1.13E-05 3.00E-04 5.92E-04

α(mRad) ΔPV(mm) ΔU(mm) 3.28E-01 4.16E-06 3.00E-04

Δn

ΔA(mm) 2.83E-06

0.00E+00

ΔnH ΔnT ΔnP -9.02E-09 -9.29E-07 2.67E-06

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Part- BINS1011 Radius(mm)- 2.60E+02

Part Dia(mm)- 3.44E+02 ΔD(mm) 7.95E-04

ΔDG(mm) ΔDI(mm) ΔDE(mm) 1.40E-05 3.00E-04 7.36E-04

α(mRad) ΔPV(mm) ΔU(mm) 3.28E-01 4.16E-06 3.00E-04

Δn

ΔA(mm) 2.83E-06

0.00E+00

ΔnH ΔnT ΔnP

-9.02E-09 -9.29E-07 2.67E-06

Figure 13/14: DMI radius of curvature measurement uncertainties

12. Error Associated with Profilometry for Radius of Curvature

Description of Profilometer: The profilometer used to verify the spherical and aspheric profiles uses a low contact force spherical probe tip. The positions of the x, y, and z axis axes are measured with distance measuring interferometers. Accuracy and Calibration of Profilometer: The profilometer is typically accurate to less than 1 um P-V over a large population of measurement points on surface of the scale of the Binospec optics, once dust spikes are removed from the data. The RMS repeatability of the data population is typically better than 1/4um. Once a week, this machine is calibrated with a one inch master ball of well known radius. During this calibration, Tinsley measures the master sphere radius along with the Peak to Valley error of the probe tip and master sphere. This data is used to determine if the probe tip requires replacement, or if the machine axes require recalibration (recalibration is typically not required). A typical set of data from two consecutive measurements on an optic is shown below. This data is an azimuthal average of a grid of acquired data.

J. Daniel 25 7/16/06

Focus Sagita Variability in Two Consecutive Measurements (0.0003mm P-V)

y = -1.96E-08x2 + 1.43E-06x

-5.00E-04

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

0 20 40 60 80 100 120 140

Half diameter (mm)

Z E

rror

(mm

) z error (mm)z error (mm)DifferencePoly. (Difference)

Figure 15: Uncertainty in profilometry characterization of radius of curvature

This data is for two measurements performed on an optic of similar size and curvature to the binospec concave surfaces. The focus term in the difference has a P-V error or 0.0003 mm. For conservatism, a larger P-V focus error is assumed purposes of establishing the radius of curvature uncertainty. Assuming a worst case error of 4 times this error (0.0012 mm P-V focus error), the following radius uncertainties can be calculated.

Print Radius of Curvature

Print Clear Aperture Radius Uncertainty for 1.2μm P-V

Profilometry Focus Error

(mm) (∅ mm) (mm)BINS-1001 209.250 298 0.00290BINS-1008 2223.332 274 0.65000BINS-1011 259.982 340 0.00370

Optic Type

Table 11: As built spherical radii as measured by profilometry The sensitivity of BINS1008 is smaller both due to its longer radius, and its smaller clear aperture.

Verification Methodology: Each SAO optic underwent final profilometry utilizing our “step” mode process on this. That is, the machine probe takes a series of discrete point measurements by moving to a measurement position, and servoing the probe in z down onto the surface, collecting position data, then servoing the probe up off the surface, and servoing x/y to the next measurement position, and repeating. In this manner, the probe is stepped across the entire optical surface which includes the surface outside the clear aperture. Scans in this way are performed along a defined x-axis and y-axis. By completing the measurements outside the clear aperture Tinsley ensures that valid data is obtained at the clear aperture. Software is then utilized to crop the data to the clear aperture for radius of curvature, conic constant, and Peak 2 Valley deviation from nominal aspheric description. The best fit radius and

J. Daniel 26 7/16/06

aspheric terms can also be calculated by optimizing these terms to best fit the measured surface profile. In this way, best fit vertex radii, conics, and deformation terms can be estimated.

13. Comparison of DMI ROC and Profilometry ROC:

To confirm the DMI derived values for radius of curvature, the surfaces were measured with profilometry. Radii were calculated for the spherical surfaces that best fit the data. The profilometry derived radii are compared to the radii measured by DMI on the following table. The differences are inside of the estimated profilometry worst case error, which is a significantly larger error than the DMI values. In general, Tinsley recommends using the DMI derived radius values where possible, as these values are generally more accurate.

Optic Type Print ROC

(mm) DMI ROC

(mm) Profilometry ROC

(mm) Difference

(Profilometry – DMI) (mm)

BINS-1001 SN1 209.250 209.2477± 6E-04 209.248 ± 0.003 0.001 BINS-1001 SN2 209.250 209.2523± 6E-04 209.250 ± 0.003 -0.003 BINS-1008 SN1 2223.332 NA 2223.4 ± 0.7 NA BINS-1008 SN2 2223.332 NA 2223.4 ± 0.7 NA BINS-1011 SN1 259.982 260.0162± 8E-04 260.0138 ± 0.004 -0.002 BINS-1011 SN2 259.982 259.9919± 8E-04 259.990 ± 0.004 -0.002

Table 12: As built spherical radii as measured by COC&DMI / profilometry

Calculation of Radius of Curvature Sag Specification for Spherical Surfaces: Calculation Method of Spherical Sag for BINS-1008:

During the conventional polishing step of the finishing process the radius of curvature of the spherical surface was controlled with a 7 inch diameter test plate. The test plate fit is quoted in the final data package for both serial number 1 and 2.

Final M5 profilometry:

Optic Name Profilometer Measured Radius [mm]

Calculated Sag over a 7 diameter relative to nominal radius [fringes

@ .633μm ] BINS-1008 sn1 2223.42 0.21 BINS-1008 sn2 2223.45 0.18

*Drawing Spec for spherical radius 2223.332 mm. Spherical Sag for BINS-1001:



Calculated Sag over a perfect 8 inch test plate

[fringes @ .633μm] BINS-1001 sn1 209.248 0.76

J. Daniel 27 7/16/06

BINS-1001 sn2 209.250 0.00 *Drawing Spec for spherical radius 209.25 mm.

Calculation Method for BINS-1011: For the concave surface of BINS-1011, identical methodology was employed to that of BINS-1001 as described above.



Calculated Sag over a perfect 7.87 inch test plate

[fringes @ .633μm] BINS-1011 sn1 260.014 2.1 BINS-1011 sn2 259.990 4.2

*Drawing Spec for spherical radius 259.982 mm

14. A and B datum definition All revolute and perpendicularity specification tolerances are identical for each optic type. As an example of this, below is from BINS-1001 Rev5 drawing.

Figure 16: A/B datums and specification of cylinder relative to A/B

Introduction: Specifications: The following is a description of the optical surface relative to the two datums laid out in the drawings for the optics above. Measurements are compiled from optical test and mechanical test data. The two datums are defined as follows:

• A-datum: The best fit axis of the aspheric surface. • B-datum: The plane perpendicular to the A-datum.

J. Daniel 28 7/16/06

Coordinate system: The relevant specifications are the runout of the cylinder relative to A, and the perpendicularity of the cylinder relative to B. The test data uses the following coordinate system to establish the polarity of the optical axis relative to part geometry:

• The line drawn from the center of the part to the scribe mark near the part name and serial number defines the positive y-axis.

• The line drawn from the center of the part extending perpendicular to the face flat and away from the concave surface defines the negative z-axis.

• The positive x-axis is defined as [+y,-z] (using the bracket notion to denote cross product). An example of this coordinate system is shown below.

• The x/y plane is in plane with the points at which the test mount touches CX surface, shown as a dashed red line in the figure below.

Figure 17: Coordinate System for the Measurement of A/B Datums

15. Optical Test Method for establishing Optical axis angle/centration

By technique, the optical test measures the centration the lens optical axis relative to two point contacts on the cylinder edge and the reference plane upon which the optic rotates. The optical test was tooled to register against three points on the convex surface. These three points define a contact circle on the cx surface shown as a red dashed line in figure 8. By using a multi-position test, the precession of the optical axis about its rotation center and plane can be characterized. Thus, the cx surface contact plane (that plane formed by the contact points between the mount and cx surface) defines the plane datum that the lens optical axis precesses about during rotation of the optic in the optical test. To calculate the lens optical axis tilt and decenter, a four position average TWF map was generated. Optic centration and tilt were maintained at the same values for all test rotational positions. The average wavefront error map was fitted for the tilt and coma zernikes over the appropriate clear apertures. Sensitivities of these tilt and coma zernikes to optic decenter and tilt were measured experimentally. A 2x2 matrix for each of the x and y directions was constructed using the measured zernikes of tilt and coma, and the sensitivities of these zernikes to optic tilt and decenter. This allowed the calculation of the best fit lens optical axis tilt and decenter relative to the cylinder of the optic and the cx surface rotational datum.

+y +z

+x

J. Daniel 29 7/16/06

The uncertainty in this measurement is measurable by the repeatability of the test configuration and is < ± 12μm centration and < ± 30 μrad radians in tilt of the optical surface. The resulting optical test data is shown below:

BINS1008-1 BINS1008-2 BINS1001-1 BINS1001-2 BINS1011-1 BINS1011-2 A Datum Centration to Cyl XCen(mm) 0.011 -0.024 0.0006 0.002 0.011 0.014 YCen(mm) -0.019 -0.009 0.008 0.004 0.001 0.018 RSS(X&Y)(mm) 0.022 0.025 0.008 0.004 0.011 0.023 Specification (mm) 0.025 0.025 0.025 0.025 0.025 0.025 Lens Optical Axis Pointing Vector Relative to CX surface X tilt (rad) -2.33E-05 3.67E-04 2.24E-05 -8.23E-05 -9.86E-05 4.11E-06 Y tilt (rad) -1.83E-04 -6.12E-05 1.20E-04 1.27E-04 7.12E-05 1.99E-04 RSS Tilt (rad) 1.84E-04 3.72E-04 1.22E-04 1.52E-04 1.22E-04 1.99E-04

Table 13: Centration and pointing of optical axis relative to cylinder and face flat The lens optical axis point vector in table 6 shows the angles that the pointing vector achieves with respect to the plane of the cx surface shown in figure 8. To determine the perpendicularity of the cylinder to the B datum, an additional mechanical measurement is made.

16. TIR of Cylinder to Datum B In this measurement, the optics are mounted on an air bearing cx side down, and the face flat and edge are indicated in to best fit run out. The face flat for all parts was found to be flat to measurement error (+/- 0.6 um). Then, the run out of the cylinder is characterized at the top and bottom of the cylinder to determine if the cylinder has any cone or tilt relative to the face flat. Finally, a TIR measurement of the CX surface is made. See figure 18 for a conceptual representation of this measurement.

Figure 18: Layout of TIR measurements

Air bearing

Indicate in

Indicate in

Measure TIR

Measure taper and tilt runout

Measure TIR

J. Daniel 30 7/16/06

The TIR of the cylinder relative to B is composed of three terms: 1) optical axis pointing vector to CX surface times cylinder length, 2) runout of cylinder relative to faceflat, and 3) angle from the CX surface runout to the face flat times the cylinder length. The first term is given in table 13. The second term is given below in table 14. Because the runout of the cylinder relative to the face flat is near perfect, the only significant terms are the runout of the cx surface relative to the faceflat (and thus the cylinder), and the pointing vector of the optical axis relative to the CX surface. In table 14 below, the angle of the optical axis relative to the cx surface is added to the angle of the cx surface (derived from its TIR to the faceflat) relative to the cylinder as a worst case assumption. The angle of the cx surface relative to the cylinder/face flat is negligible compared to the angle of the optical axis relative to the CX surface. That is, the cylinder run out relative to B is dominated by just the term of the optical axis relative to the cx surface. All these values compare favorably against the 25 um requirement.

BINS1008-1 BINS1008-2 BINS1001-1 BINS1001-2 BINS1011-1 BINS1011-2

Cylinder Run Out Relative to Face Flat

x(mm)- 2E-04 0E-04 0E-04 1E-04 1E-04 5E-04

y(mm)- 0E-04 3E-04 0E-04 1E-04 1E-04 -1E-04

RSS(mm)- 2E-04 3E-04 0E-04 1E-04 1E-04 5E-04

CX Surface Run Out Relative to Face Flat and resulting cylinder runout

CX Surf TIR (mm) 6E-4 6E-3 4E-3 10E-3 5E-3 11E-3

∅CA(mm) 274 274 298 298 320 320 CX Surf angularity to face flat (rad) 2E-6 2E-5 1.3E-5 3.4E-5 1.6E-5 3.4E-5 Cylinder Contact (mm) 2.79E+01 2.79E+01 5.21E+01 5.21E+01 5.21E+01 5.21E+01

Total TIR Cylinder to B

(mm)- 5.1E-03 10E-03 6.4E-03 7.9E-03 6.4E-03 10E-03

Table 14: Cylinder Taper & Tilt Run Out Relative to Face Flat

17. Axial Runout of Spherical Surface with Respect to Datum B

The axial runout requirement of the spherical surface with respect to datum B is 0.015mm. Datum B is the optical axis of the aspheric surface. This axis is not directly measured in Tinsley’s test, as Tinsley’s test only checks the optical axis of the entire lens element. The tilt angles shown in table 6 are for the entire lens. To estimate the conversion of the lens best fit optical axis angle (as measured in the Tinsley test) to the best fit optical axis angle of the aspheric surface, the following analysis was done.

J. Daniel 31 7/16/06

Experimental sensitivities were generated for the relationship between lens tilt and decenter and wavefront tilt and coma for the BINS1001/1008/1011 elements. C2 is the tilt zernike coefficient. C7 is the coma zernike coefficient. These values were confirmed with the construction of a ray trace model of the null tests. Then, the sensitivity of wavefront tilt and coma were calculated to the aspheric surface tilt and decenter. In general, the test wavefront generates larger values (degrades more) for a given tilt of the aspheric surface, relative to the wavefront generated from the same tilt of the entire lens. The effective tilt of the optical axis of the aspheric surface is estimated by multiplying the measured RSS tilt term in table 13 by the ratio of the lens coma sensitivity to tilt to the aspheric surface coma sensitivity to tilt. This value is then multiplied by the spherical clear aperture, and added to the TIR of the spherical surface, relative to the convex surface. For BINS 1008, the CX surface is the spherical surface, so there is no additional contribution. For BINS1001 and BINS1011, the CC surface is the sphere. For example, for BIN1001-1, the spherical surface TIR to the B datum is 1.22e-4*298+.004= .032 mm. This is a worse case TIR, as the magnitudes of the TIR contributions were added, and any cancellation from vector contribution of the two TIR’s was not considered. The spherical surface clear apertures are 298mm, 274mm, and 320mm respectively for BINS1001, 1008, and 1011. This is shown in Table 15 below for the BINS1011 elements. For example the tilt of the spherical surface relative to the axis of the aspheric surface optical axis is calculated by 1.22e-4*320mm*(28/3.74)= .010 mm. 320mm is the CA of BINS1011.

Decenter and Tilt of Lens Tilt of AsphereOptical Axis Tilt

Spherical Surface TIR

Ray Trace Model (OSLO)

Experimental Data


rss tilt (rad) (mm)

Zernike Fringe Polynominal 2 pass dC2/dy (wv/μm) 0.393 0.45

BINS1011 SN1 lens tilt 1.22E-04

Zernike Fringe Polynominal 2 pass dC7/dy (wv/μm) -0.040 -0.046


Zernike Fringe Polynominal 2 pass dC2/drx (wv/mrad) -34.40 -35.5 -185

BINS1011 SN1 effective asph surf tilt 1.63E-05 0.010

Zernike Fringe Polynominal 2 pass dC7/drx (wv/mrad) 3.73 3.74 28


BINS1011

Table 15: BINS1011 Spherical Surface TIR relative to optical axis angle of aspheric surface

Tables 16 and 17 contain the values for BINS1001 and BINS1008. Unlike in the BINS1011 case, there is some disagreement in the values of the Zernike terms seen experimentally from tilts and decenters in comparison to those predicted in ray tracing. The source of this disagreement is not understood. The key relationship between experimental coma from lens tilt, and ray trace coma from lens and aspheric surface tilt appears to be consistent for BINS1001. Thus, the spherical surface TIR, which depends on these values, is reliable. For BINS1008, The ratio of coma induced by aspheric surface tilt to coma induced by lens tilt seems quite low. Thus, the spherical surface TIR in these elements is probably artificially high. It is in spec in one case, and relatively close to spec in the other, nonetheless.

J. Daniel 32 7/16/06




Experimental Data


rss tilt (rad) (mm)





Zernike Fringe Polynominal 2 pass dC2/drx (wv/mrad) -26.00 -43.6 -152.5


Zernike Fringe Polynominal 2 pass dC7/drx (wv/mrad) 3.05 3.40 7.85


BINS1001





Experimental Data


rss tilt (rad) (mm)





Zernike Fringe Polynominal 2 pass dC2/drx (wv/mrad) -34.40 -23.6 -154.5


Zernike Fringe Polynominal 2 pass dC7/drx (wv/mrad) 3.73 -0.94 16


BINS1008


18. Physical Runout of Surfaces Table 18 contains the physical runouts of the surfaces of the elements.

BINS1008-1 BINS1008-2 BINS1001-1 BINS1001-2 BINS1011-1 BINS1011-2 CC Surface TIR to face flat (mm) +.001 +.001 +0.008 +0.001 +.001 +.006 CC High TIR azimuth (deg) 200 80 45 220 45 320 CX Surface TIR to face flat (mm) +.001 +.004 +.004 +.004 +.005 +.011 CX High TIR azimuth 180 90 225 250 315 220

Table 18: CC/CX surface runouts relative to face flat

TINSLEY

FINAL TEST DATA (precoat)

SAO Binospec

BINS1001 Collimator Lens 1 s/n 001

a subsidiary of SSGPO

Collimator Lens 1Sn-001

01-18-06

SAO BinoSpec BINS-1001 Final Test Data

Program Manager:

Darius Moily

Metrology Supervisor:

John Van de Wall

Quality Supervisor:

Pat Catron

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a subsidiary of SSGPOTinsley Confidential Information - BINS1001 s/n 001 2

Concave/Spherical Wavefront Test Layout

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Concave/Spherical Wavefront Test Layout (cont.)

• Controlled Test Temperature = 24 °C +/- 2 °C. Final Optical test completed at 23 °C. • Lens is mounted on a stable 5-axis mount with the concave surface facing the

interferometer.• The 5-axis mount is calibrated to move away from the interferometer on the optical axis

to within 0.2 milli-Radians.• WFE is measured using a Fizeau interferometer.• Distance is measured using a Distance Measuring Interferometer (DMI).

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Radius of Curvature Test Procedure for Spherical Surface• Bring Lens to the Cat’s Eye of f/0.65 diverger.• Adjust x/y of the Lens to center the Lens relative to the source spot.• Move the lens to the Radius of Curvature position. Adjust rx/ry of the lens until the

radius of curvature falls onto the source spot. • Iterate between the previous two steps until motion along z does not require

adjustment at the two points.• Zero DMI• Set lens to radius of curvature.• Phase surface with interferometer. Record focus Zernike term and DMI reading.• Move lens to Cat’s Eye position of f/0.65 diverger.• Phase surface map with interferometer. Record focus Zernike term and DMI

reading. • Repeat the previous four steps until a good distribution is obtained.• Plot Focus vs. DMI reading for each phase position. Assuming a low order linear fit

calculate where Focus = 0 for each position. The radius of curvature of the surface is then given by the difference in the Z value at each of these positions.

Measured Radius of Curvature = 8.2381 inches (209.248 mm) or 1.0 fringes ± 0.25 fringesover a characteristic 8 inch test plate.

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Concave/Spherical Wavefront Test Procedure

• Position the lens at the Cat’s Eye of the interferometer.• Rotate lens to nominal test position (ie. Primary test fiducial at +y).• Center lens relative the source point.• Move lens to radius of curvature and best null fringe pattern. By adjustment of the

five axis mount.• Register four optical test fiducials (starting with fiducial at +y and continuing

clockwise) and phase WFE.• Rotate lens 90 degrees and repeat previous step. Continue until part has been

phased in four 90 degree positions.• Average four WFE files with registration of test fiducials.

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Final Concave/Spherical WFE

Surface figure for spherical surface is 0.025 waves RMS

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Concave/Spherical Surface:10X Phase Measuring Microscope Subaperture Locations

• Site 1) Rq = 19.6 A RMS• Site 2) Rq = 18.8 A RMS• Site 3) Rq = 18.1 A RMS• Site 4) Rq = 17.5 A RMS• Site 5) Rq = 17.9 A RMS

Subaperture size = 1.4 mm2

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Position 1, R = 0.5 cm

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Asphere Wavefront Test Layout

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Asphere wavefront test layout (cont.)


interferometer.• The 5-axis mount is calibrated to move away from the interferometer on the optical

axis to within 0.2 milli-Radians.• WFE is measured using a Fizeau interferometer.

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Asphere Wavefront Test Procedure:

• Position Lens in 5-axis mount with concave surface facing interferometer. • Rotate lens to nominal position (primary optical test fiducial at +y).• Position Lens at 924.6 mm beyond source position.• The CGH forms a spot at the vertex of the concave surface at the nominal z position.

Adjust x/y of lens until this spot is centered on lens surface.• Position CGH BINS1001 in 5-axis mount with lettering facing interferometer.• Remove diverger. Adjust rx/ry of CGH as if testing a flat.• Replace diverger. Move CGH to approximately 90 mm toward interferometer from

source and look for alignment feature. Adjust x/y/z of CGH to best null fringes of CGH.• The CGH forms a spot at the vertex of the concave surface at the nominal z position.

Adjust x/y of lens until this spot is centered on lens surface.

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Asphere Wavefront Test Procedure (cont.)

• Move retrosphere to 78.6 mm beyond aspheric surface of lens. • Isolate first order diffraction spot from CGH using a 3mm aperture.• Fine adjust rx/ry of lens and retrosphere until WFE is best nulled.• Register four optical test fiducials starting with primary fiducial and continuing

counterclockwise.• Phase WFE. Rotate part through 90 degrees and continue previous step.• Repeat previous two steps until four phase maps at 90 degree intervals have been

taken.• Average four files with fiducial registration.

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Final Aspheric WFE Over the Clear Aperture

RMS Transmitted WFE = 0.038 wv over CA

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Final Slope Error Statistics of WFE•• SVG/Tinsley Inc. ****************************** Date: Jan 18 '06 Wed• Task #: 010 SLOPE ANALYSIS PROGRAM Time: 13:34:28 • Work #: 4436 ****************************** User: TR •• REMARK: Sao Binospec Collimator Lens1 Sn-001•• METHOD: Calculate SQRT((dz/dx)**2 + (dz/dy)**2)) by nearest neighbors•• INPUT: Filename 0118S1F.FIL ( @@@@05 gint), created on Jan 18 06 • Spacing x = 0.524 Center x = 0.000 Size x = 655• y = 0.524 y = 0.000 y = 655• Min z = -0.00011 Max z = 0.00016 P-V z = 0.000270• Min r = 0.00000 Max r =152.73069 • Units x,y : mm z : mm Points = 264736

• APERTURE: No aperture,all data accepted• 1 data points excluded, 264735 data remaining.• No obscuration

• OUTPUT: No percent area excluded from slope analysis, all data accepted• Slope tolerance setting = 5 urad• Nearest spacings used in slope calculations x: 0.5235 mm• y: 0.5235 mm• Slope map saved in SLOPE2.@05, total 264735 valid points

• Final slope statistics: RMS= 4.5641 urad NPT=264735 • P-V= 189.1530 urad AVG=2.967 urad

RMS Slope Error = 4.56 μrad over CA

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Aspheric Surface 10X PMM Spot Locations



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7/21/2006 TINSLEY LABORATORIES, INC. I

CUSTOMER Smithsonian Astrophysical Observatory P.O. # SK4-04002 JOB # 4436 PART # BINS-1001 (PRE-COATED) PART NAME: LENS 1, Collimator

S/N:001 BLUEPRINT TOLERANCE

BLUEPRINT DIMENSION

ACTUAL SIZE

LOCATION

+/-.05 316.00 315.96 mm O.D.

TIR Cylinder to A 0.025 A .008 mm Runout

Perp. Cyl. To B ┴ 0.025 B .006 mm Perpendicularity

+/-.2 15.242 15.364 mm CT

+.25/-.00 64.76 64.84 mm CC Sag

+/-.25 1.00 1.14 mm Bevel CC Side

+/-5.0 45º 45º Bevel CC Side

+/-.25 1.00 1.14 mm Bevel CX Side

+/-5.0 35º 35º Bevel CX Side

Workmanship Conform Note:2

60/40 Conform Note: 5 Surface Qualty

<30Å 18.4Å Note: 6 Surface Roughness (CC)

<30Å 19.4Å Note: 6 Surface Roughness (CX)

≤ 4 Fr. 209.2477 mm Note:7 Radius Curvature

<5 μrad 4.56 μrad Slope Error

<.05λ .038λ Transmitted Wavefront Figure

±0.167 fringe <±0.167 ±0.081 Spherical Surface Figure

Note 10 <15 um 20um Spherical Surface TIR to Datum B

REMARKS: ACCEPTED BY: _______________________ DISCREPANCY TAG NUMBER: _____________________

TINSLEY


SAO Binospec




01-20-06


Program Manager:

Darius Moily


John Van de Wall

Quality Supervisor:

Pat Catron

1 1/2

8/04



1 1/2

8/04







Measured Radius of Curvature = 8.23828 inches (209.252 mm) or 1.0 fringes ± 0.25 fringesover a characteristic 8 inch test plate.

1 1/2

8/04







1 1/2

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• Position Lens in 5-axis mount with concave surface facing interferometer. • Rotate lens to nominal position (primary optical test fiducial at +y).• Position Lens at 924.6 mm beyond source position.• The CGH forms a spot at the vertex of the concave surface at the nominal z

position. Adjust x/y of lens until this spot is centered on lens surface.• Position CGH BINS1001 in 5-axis mount with lettering facing interferometer.• Remove diverger. Adjust rx/ry of CGH as if testing a flat.• Replace diverger. Move CGH to approximately 90 mm toward interferometer from

source and look for alignment feature. Adjust x/y/z of CGH to best null fringes of CGH.

• The CGH forms a spot at the vertex of the concave surface at the nominal z position. Adjust x/y of lens until this spot is centered on lens surface.

1 1/2

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• Move retrosphere to 78.6 mm beyond aspheric surface of lens. • Isolate first order diffraction spot from CGH using a 3mm aperture.• Fine adjust rx/ry of lens and retrosphere until WFE is best nulled.• Register four optical test fiducials starting with primary fiducial and continuing

counterclockwise.• Phase WFE. Rotate part through 90 degrees and continue previous step.• Repeat previous two steps until four phase maps at 90 degree intervals have been


1 1/2

8/04




1 1/2

8/04


Final Slope Error Statistics of WFE


• SVG/Tinsley Inc. ****************************** Date: Jan 23 '06 Mon• Task #: 010 SLOPE ANALYSIS PROGRAM Time: 15:05:06 • Work #: 4436 ****************************** User: TR •• REMARK: Sao Binospec Collimator Lens1 Sn-002•• METHOD: Calculate SQRT((dz/dx)**2 + (dz/dy)**2)) by nearest neighbors•• INPUT: Filename 0123S2F.FIL ( @@@@05 gint), created on Jan 23 06 • Spacing x = 0.524 Center x = 0.000 Size x = 655• y = 0.524 y = 0.000 y = 655• Min z = -0.00012 Max z = 0.00006 P-V z = 0.000176• Min r = 0.00000 Max r =152.73069 • Units x,y : mm z : mm Points = 264869

• APERTURE: No aperture,all data accepted• No obscuration



1 1/2

8/04






CUSTOMER Smithsonian Astrophysical Observatory P.O. # SK4-04002 JOB # 4436 PART # BINS-1001 (PRE-COATED) PART NAME: LENS 1, Collimator


BLUEPRINT DIMENSION

ACTUAL SIZE

LOCATION

+/-.05 316.00 315.98 mm O.D.

TIR Cylinder to A 0.025 A .005 mm Runout

Perp. Cyl. to B ┴ 0.025 B .008 mm Perpendicularity

+/-.2 15.242 15.347 mm CT

+.25/-.00 64.76 64.87 mm CC Sag

+/-.25 1.00 1.14 mm Bevel CC Side

+/-5.0 45º 45º Bevel CC Side

+/-.25 1.00 1.01 mm Bevel CX Side

+/-5.0 35º 35º Bevel CX Side











TINSLEY


SAO Binospec




12-29-05


Program Manager:

Darius Moily


John Van de Wall

Quality Supervisor:

Pat Catron

1 1/2

8/04



Transmission Sphere F1.5

1 1/2

8/04


Asphere Wavefront Test Layout (cont.)



axis to within 0.2 milli-Radians.• WFE is measured using a Fizeau interferometer with Test wedge factor = +0.5.

1 1/2

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• Position of retro-sphere at the cat’s eye of the interferometer. Center retro-sphere relative to the source.

• Position retro-sphere at it’s radius of curvature and adjust rx/ry to best null wavefront of retro-sphere. Move retro-sphere clear of setup.

• Position lens in 5-axis mount with concave surface facing interferometer in nominalrotation (Primary optical fiducial at +y).

• Position lens at cat’s eye and adjust x/y until lens is centered relative to the source.• Move lens to radius of curvature of concave surface. Adjust rx/ry to best null

wavefront. • Position the lens to 588 mm beyond the source position. • Position CGH Bins-1008 in 5-axis mount with lettering facing interferometer.• Remove diverger. Adjust rx/ry of CGH as if testing a flat.• Replace diverger. Move CGH to cat’s eye. Adjust x/y until source is centered on

CGH surface pattern. • Move CGH to 200 mm and continue adjustment of x/y/z of CGH until fringes of CGH

outer ring nulls.

1 1/2

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• Move retro-sphere to 100.77 mm beyond aspheric surface of lens. Fine adjust rx/ry/x/y of lens and retro-sphere until WFE is best nulled.

• Register four optical test fiducials starting with primary fiducial and continuing counterclockwise.

• Phase WFE. Rotate part through 90 degrees and continue previous step.• Repeat previous two steps until four phase maps at 90 degree intervals have been


1 1/2

8/04


Final Transmitted WFE Over the Clear Aperture


1 1/2

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Final Slope Error Statistics of Transmitted WFE• SVG/Tinsley Inc. ****************************** Date: Nov 30 '05 Wed• Task #: 010 SLOPE ANALYSIS PROGRAM Time: 11:24:20 • Work #: 4436 ****************************** User: TR •• REMARK: SaoCol8 Sn-001•• METHOD: Calculate SQRT((dz/dx)**2 + (dz/dy)**2)) by nearest neighbors•• INPUT: Filename 1020S1AZ.CRP ( @@@@05 gint), created on Oct 20 05 • Spacing x = 1.200 Center x = 0.000 Size x = 300• y = 1.200 y = 0.000 y = 300• Min z = -0.00006 Max z = 0.00009 P-V z = 0.000155• Min r = 0.84853 Max r =133.65059 • Units x,y : mm z : mm Points = 37988


• OUTPUT: No percent area excluded from slope analysis, all data accepted• No slope tolerance specified• Nearest spacings used in slope calculations x: 1.2000 mm• y: 1.2000 mm• Slope map saved in SLOPE2.@05, total 37988 valid points


• RMS Slope Error = 4.52 μrad over CA

1 1/2

8/04


Concave Aspheric Surface:10X Phase Measuring Microscope Subaperture Locations

• Site 1) Rq = 6.7 A RMS• Site 2) Rq = 7.4 A RMS• Site 3) Rq = 23 A RMS• Site 4) Rq = 6.7 A RMS• Site 5) Rq = 6.1 A RMS


R

1 1/2

8/04



1 1/2

8/04


Convex Surface:10X Phase Measuring Microscope Subaperture Locations



R

Test plate fit to convex surface is 1 fringe concave with 0.25 fringes of uncertainty.

1 1/2

8/04




CUSTOMER Smithsonian Astrophysical Observatory P.O. # SK4-04002 JOB # 4436 PART # BINS-1008 (PRE-COATED) PART NAME: LENS 8, COLLIMATOR


BLUEPRINT DIMENSION

ACTUAL SIZE

LOCATION

+/-.05 286.00 285.97 4D O.D.

TIR Cylinder to A 0.025 A .0216 mm 4D Runout

Perp. Cyl. To B ┴ 0.025 B .005 mm 4D Perpendicularity

+/-.2 16.834 16.787 1C CT

+.25/-.00 15.96 15.96 1B CC Sag

+/-.25 1.00 1.00 B5 Bevel CC Side

+/-5.0 45º 45º B5 Bevel CC Side

+/-.25 1.00 1.00 B3 Bevel CX Side

+/-5.0 43º 43º B3 Bevel CX Side

TIR 0.015 B <.001 C3

Workmanship * Note:2




≤ 4 Fr. 2223.4 mm. Note:7 Radius Curvature



±0.167 fringe <±0.167 Spherical Surface Figure

Coating **N/A Note: 11


* Accept per D. Fabricant email dated 12/23/05 ** Part is Before Coating


TINSLEY


SAO Binospec




12-29-05

Program Manager:

Darius Moily


John Van de Wall

Quality Supervisor:

Pat Catron


1 1/2

8/04



Transmission Sphere F1.5

1 1/2

8/04



• Controlled Test Temperature = 24 °C +/- 2 °C. Final Optical test completed at 23 °C • Lens is mounted on a stable 5-axis mount with the concave surface facing the



1 1/2

8/04


Asphere Wavefront Test Procedure

• Position IOA retro-sphere at the cat’s eye of the interferometer. Center retro-sphere relative to the source.




wavefront. • Position the lens to 588 mm beyond the source position. • Position CGH Bins-1008 in 5-axis mount with lettering facing interferometer.• Remove diverger. Adjust rx/ry of CGH as if testing a flat.• Replace diverger. Move CGH to cat’s eye. Adjust x/y until source is centered on


outer ring nulls.

1 1/2

8/04



• Move retrosphere to 100.77 mm beyond aspheric surface of lens. Fine adjust rx/ry/x/y of lens and retrosphere until WFE is best nulled.




1 1/2

8/04



Final Transmitted WFE Over the Clear Aperture

1 1/2

8/04


Final Slope Error Statistics of Final WFE


• SVG/Tinsley Inc. ****************************** Date: Dec 28 '05 Wed• Task #: 010 SLOPE ANALYSIS PROGRAM Time: 19:14:26 • Work #: 4436 ****************************** User: TR •• REMARK: Sao Binospec Col Lens 8 Sn-002•• METHOD: Calculate SQRT((dz/dx)**2 + (dz/dy)**2)) by nearest neighbors•• INPUT: Filename 1228C2F.FIL ( @@@@05 gint), created on Dec 28 05 • Spacing x = 0.519 Center x = 0.000 Size x = 685• y = 0.519 y = 0.000 y = 685• Min z = -0.00008 Max z = 0.00010 P-V z = 0.000184• Min r = 0.00000 Max r =132.72225 • Units x,y : mm z : mm Points = 203137



• Final slope statistics: RMS= 4.8478 urad NPT=203137

•

1 1/2

8/04


Aspheric Surface:10X Phase Measuring Microscope Subaperture Locations



1 1/2

8/04



1 1/2

8/04


Spherical Surface:10X Phase Measuring Microscope Subaperture Locations

Test plate fit to convex surface is 2 fringes convex with 0.25 fringes of uncertainty

• Site 1) Rq = 5.1 A RMS• Site 2) Rq = 4.6 A RMS• Site 3) Rq = 4.6 A RMS• Site 4) Rq = 5.3 A RMS • Site 5) Rq = 4.8 A RMS


1 1/2

8/04




CUSTOMER Smithsonian Astrophysical Observatory P.O. # SK4-04002 JOB # 4436 PART # BINS-1008 (PRECOATED) PART NAME: LENS 8, COLLIMATOR


BLUEPRINT DIMENSION

ACTUAL SIZE

LOCATION

+/-.05 286.00 286.00 4D O.D.



+/-.2 16.834 16.871 1C CT

+.25/-.00 15.96 16.053 1B CC Sag

+/-.25 1.00 1.14 B5 Bevel CC Side


+/-.25 1.00 1.14 B3 Bevel CX Side


TIR 0.015 B <.015 C3


60/40 *Non-Conform Note: 5 Surface Qualty




<5 μrad 4.85 Slope Error

<.05λ .039 Transmitted Wavefront Figure

±0.167 fringe <±0.167 Spherical Surface Figure



* Accept per D. Fabricant email dated 12/12/05 ** Part is before Coating


TINSLEY


SAO Binospec

BINS1011 Camera Lens 1 s/n 001


Camera Lens 1Sn-001

12-29-05


Program Manager:

Darius Moily


John Van de Wall

Quality Supervisor:

Pat Catron

1 1/2

8/04



1 1/2

8/04







Measured Radius of Curvature = 10.236 inches (259.994 mm) or 3.5 fringes ± 0.5 fringes

1 1/2

8/04







1 1/2

8/04







wavefront. • Position the lens to 1034.959 mm beyond the source position. • Position CGH Bins-1011 in 5-axis mount with lettering facing interferometer.• Remove diverger. Adjust rx/ry of CGH as if testing a flat.• Replace diverger. Move CGH to cat’s eye. Adjust x/y until source is centered on


outer ring nulls.

1 1/2

8/04



• Move retrosphere to 46.4 mm beyond aspheric surface of lens. Fine adjust rx/ry/x/yof lens and retrosphere until WFE is best nulled.




1 1/2

8/04




** Ring zones are largely due to ghost fringes and are not polished into the optic due to Tinsley’s smoothing technique.

1 1/2

8/04



• SVG/Tinsley Inc. ****************************** Date: Dec 28 '05 Wed• Task #: 010 SLOPE ANALYSIS PROGRAM Time: 17:47:55 • Work #: 4436 ****************************** User: TR •• REMARK: Sao Binospec Camera Lens1 Sn-001•• METHOD: Calculate SQRT((dz/dx)**2 + (dz/dy)**2)) by nearest neighbors•• INPUT: Filename 1228S1F.FIL ( @@@@05 gint), created on Dec 28 05 • Spacing x = 0.611 Center x = -9.525 Size x = 655• y = 0.611 y = 0.364 y = 625• Min z = -0.00016 Max z = 0.00007 P-V z = 0.000229• Min r = 0.34961 Max r =172.84377 • Units x,y : mm z : mm Points = 249115





1 1/2

8/04






CUSTOMER Smithsonian Astrophysical Observatory P.O. # SK4-04002 JOB # 4436 PART # BINS-1011 (PRE-COATED) PART NAME: LENS 1, CAMERA


BLUEPRINT DIMENSION

ACTUAL SIZE

LOCATION

+/-.05 358.00 358.02 4D O.D.



+/-.2 15.241 15.443 1C CT

+.25/-.00 65.00 65.07 1B CC Sag

+/-.25 1.00 .89 B5 Bevel CC Side


+/-.25 1.00 1.02 B3 Bevel CX Side


TIR 0.015 B <.015 C3











** Part is Before Coating


TINSLEY


SAO Binospec

BINS1011 Camera Lens 1 s/n 002


Camera Lens 1Sn-002

12-29-05


Program Manager:

Darius Moily


John Van de Wall

Quality Supervisor:

Pat Catron

1 1/2

8/04


Concave Wavefront Test Layout

1 1/2

8/04


Concave Wavefront Test Layout (cont.)

• Controlled Test Temperature = 24 °C +/- 2 °C. Final Optical test completed at 23.9 °C. • Lens is mounted on a stable 5-axis mount with the concave surface facing the



1 1/2

8/04


Radius of Curvature Test Procedure

• Bring Lens to the Cat’s Eye of f/0.65 diverger.• Adjust x/y of the Lens to center the Lens relative to the source spot.• Move the lens to the Radius of Curvature position. Adjust rx/ry of the lens until the

radius of curvature falls onto the source spot. • Iterate between the previous two steps until motion along z does not require adjustment

at the two points.• Zero DMI• Set lens to radius of curvature.• Phase surface with interferometer. Record focus Zernike term and DMI reading.• Move lens to Cat’s Eye position of f/0.65 diverger.• Phase surface map with interferometer. Record focus Zernike term and DMI reading. • Repeat the previous four steps until a good distribution is obtained.• Plot Focus vs. DMI reading for each phase position. Assuming a low order linear fit


Measured Radius of Curvature = 10.236 inches (259.994 mm) or 3.5 fringes ±0.5 fringes over a 8.46 inch test plate.

1 1/2

8/04


Concave Wavefront Test Procedure





1 1/2

8/04




1 1/2

8/04



• Site 1) Rq = 26.4 A RMS• Site 2) Rq = 27 A RMS• Site 3) Rq = 26.1 A RMS• Site 4) Rq = 26 A RMS• Site 5) Rq = 26 A RMS


1 1/2

8/04



1 1/2

8/04


Asphere Wavefront Test Procedure





wavefront. • Position the lens to 1034.959 mm beyond the source position. • Position CGH Bins-1011 in 5-axis mount with lettering facing interferometer.• Remove diverger. Adjust rx/ry of CGH as if testing a flat.• Replace diverger. Move CGH to cat’s eye. Adjust x/y until source is centered on


outer ring nulls.

1 1/2

8/04


Asphere wavefront test procedure (cont.)

• Move retrosphere to 46.4 mm beyond aspheric surface of lens. Fine adjust rx/ry/x/yof lens and retrosphere until WFE is best nulled.




1 1/2

8/04




** Ring zones are largely due to ghost fringes and are not polished into the optic due to Tinsley’s smoothing technique.

1 1/2

8/04



• SVG/Tinsley Inc. ****************************** Date: Dec 27 '05 Tue• Task #: 010 SLOPE ANALYSIS PROGRAM Time: 13:14:24 • Work #: 4436 ****************************** User: TR •• REMARK: Sao Camera 1 Sn-002 Final Test 12-27-05•• METHOD: Calculate SQRT((dz/dx)**2 + (dz/dy)**2)) by nearest neighbors•• INPUT: Filename 1227S2F.FIL ( @@@@05 gint), created on Dec 27 05 • Spacing x = 0.611 Center x = -9.525 Size x = 655• y = 0.611 y = 0.364 y = 625• Min z = -0.00015 Max z = 0.00013 P-V z = 0.000272• Min r = 0.34961 Max r =172.84377 • Units x,y : mm z : mm Points = 249041





1 1/2

8/04


Aspheric Surface:10X Phase Measuring Microscope Subaperture Locations

• Site 1) Rq = 13.9 A RMS• Site 2) Rq = 13.8 A RMS• Site 3) Rq = 13.9 A RMS• Site 4) Rq = 16.3 A RMS


1 1/2

8/04




CUSTOMER Smithsonian Astrophysical Observatory P.O. # SK4-04002 JOB # 4436 PART # BINS-1011 (PRE-COATED) PART NAME: LENS 1, CAMERA


BLUEPRINT DIMENSION

ACTUAL SIZE

LOCATION

+/-.05 358.00 358.00 4D O.D.



+/-.2 15.241 15.293 1C CT

+.25/-.00 65.00 65.15 1B CC Sag

+/-.25 1.00 .89 B5 Bevel CC Side


+/-.25 1.00 1.01 B3 Bevel CX Side


TIR 0.015 B <.015 C3









Coating *N/A Note: 11


* Part is Before Coating


TINSLEY

Profilometer

Optimizer Input Menus

Smithsonian Astrophysical Observatory Specification BINS-ASP Aspheric Lenses for the Binospec Spectrograph September 22, 2004 Revision 2 Daniel Fabricant [email protected] Phone: 617 495-7398 FAX: 617 495-7467

1 Introduction Binospec is a binocular optical spectrograph that uses a refractive collimator to form an ~200 mm pupil on a diffraction grating, and a refractive camera to image the dispersed light onto a CCD imaging array. Each of Binospec's identical channels contains 19 lenses, for a total of 38. The collimator contains nine lenses in three groups, and the camera contains ten lenses in four groups. Two of the collimator lenses, and one of the camera lenses, carry aspheric surfaces with 4th, 6th and 8th order terms added to a base (spherical) surface. SAO needs to procure a total of six aspheric lenses. Only one surface of each lens is aspheric; the facing surface is polished to a sphere. SAO wishes to purchase completed lenses with both surfaces polished to our specifications, and a broad band antireflection coating applied to the aspheric surfaces. SAO will supply the lens blanks; one spare blank has been purchased for each pair of lenses. The specifications for the spherical surfaces, the desired form of the aspherics and the mechanical properties of the lenses are specified on the lens drawings: BINS-1001, BINS-1008, and BINS-1011. This document details testing procedures and tolerances for the aspheric surfaces.

Figure 1 Binospec Collimator. The converted MMT's focal surface is at the upper left. Collimated light emerges from the last CaF2 lens at the right, striking the grating at the lower right.

MMT focal surface aspheric surface

grating

aspheric surface

Figure 2 Binospec Camera. The grating is at the left and the final spectrograph focus is the right.

2 Testing Techniques We expect that each aspheric lens will be tested in transmission, using a spherical reference and a holographic null lens, supplemented by surface roughness measurements. In addition, we prefer that profilometer scans be made of the aspherical surfaces to independently verify that the specified aspheric shape is achieved. The accuracy of the profilometer scans will probably not be sufficient to verify the surface figure accuracy to the level that we specify. Prospective vendors shall specify what profilometer capability they possess or have access to. In addition, the spherical surfaces of each lens will be tested with a test plate. For the two collimator lenses the test plate should be at least 175 mm in diameter, and for the camera lens the test plate should be at least 200 mm in diameter. The radii of curvature of the test plates should agree with the radii of curvature specified on the drawings to 0.025% or better accuracy and be manufactured to 0.1 wave (reference wavelength 6328 Å) PV surface quality. The minimum surface quality of the spherical surfaces of the lenses as tested against the test plates is specified on the drawings.

grating

aspheric surface

final spectrograph focus

3 Surface Figure The single-pass transmitted wavefront deviation from nominal shall be less than 0.05 waves RMS (reference wavelength 6328 Å) over the entire clear aperture.

4 Surface Roughness and Slope Errors On scales of 1 mm and less, the surface roughness shall be less than 30 Å RMS. On any scale up to the full lens aperture, the RMS slope errors shall be less than 5x10-6 radians. Prospective vendors shall specify how these surface roughness and slope error measurements will be made, and specify the spatial resolution of the proposed measurement.

5 Antireflection Coating Specifications There are three lenses that carry aspherical surfaces in each of Binospec's two identical channels, or six in total. Each of these lenses has an aspherical surface and a spherical surface. The aspherical surface faces air and must be antireflection coated to maximize the light transmitted through the optics and to minimize the effect of ghost images and scattered light; the spherical surface faces coupling fluid and does not need an antireflection coating. Since the Binospec lenses are coupled with Cargille Laboratories's Laser Liquid 5610 (LL5610), the coated surfaces may come into contact with this siloxane liquid. SAO therefore specifies an antireflection coating that can be cleaned of LL5610 spills. SAO will work with the coating vendor to test compatibility of the coating with LL5610 if coating samples are provided on witness samples SAO's additional specifications are to ensure that the antireflection coatings are stable under normal operating conditions.

5.1 Coating Performance

Antireflection Coating Performance (375nm to 1000nm, average of S&P polarizations)

5° Incidence Angle 25° Incidence Angle Peak Reflectivity 1.5% 2% Average Reflectivity <1% <1.25% Absorption < 0.25% No radioactive materials shall be used in the lens coatings. The uniformity of the coatings should be better than ±0.15%. SAO will work with the coating vendor to

optimize the coatings within the design constraints of the vendor with the objective of minimizing the risk of meeting the performance in the table above.

5.2 Coating Performance Testing The coating performance shall be verified with witness samples arranged so as to approximate the curvature of the lenses, and measured at angles near 5° and 25° incidence.

5.3 Coating Durability Cleaning: the coatings shall survive without damage 25 gentle cleanings with a cotton swab wetted with ethyl alcohol, isopropyl alcohol, acetone, or a mild detergent solution. Loose grit will be removed first with a gentle flushing of dry nitrogen gas. Adhesion: a piece of 1 cm wide cellophane tape is pressed firmly onto the coated surface. If the tape is quickly removed at an angle normal to the surface, the coatings shall show no signs of removal. Resistance to Chemicals: the coatings shall survive without damage 25 brief (10 minutes or less) wettings with water, ethyl alcohol, isopropyl alcohol, or acetone. The coating shall survive without damage for one month in contact with Cargille Laboratories' LL5610 (formulation with nD=1.5000 at 25 °C), a siloxane liquid. This liquid is used as a coupling fluid between Binospec's lenses. Operating Conditions: the coatings shall survive without damage lens temperatures between -20 °C and +20 °C at 95% or lower relative humidity. The mountain-top environment of the MMT is typically high in ozone, and this shall not damage the coatings.

6 Documentation Documentation shall be supplied with each of the six completed lenses. This documentation shall contain measurements of each of the specified dimensions on the drawings (reference dimensions are excluded), and test data that establishes that the specifications in Sections 2 through 5 are met.

final report cover - · 2007-11-30 · final report (pre-coat) sao binospec contract # sk4-04002...

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