Measurement Uncertainty for Automatic Alignment Algorithm

Presentation toLLNL CASIS Workshop

Abdul Awwal, Clement Law and Walter FergusonAutomatic Alignment & Imaging Team

National Ignition Facility (NIF), Laser Engineering division (LED)Lawrence Livermore National Laboratory

November 16-17, 2006

UCRL-PRES-226162

The work was performed under the auspices of the U.S. Department of Energy National Nuclear Security Administration by the University of California Lawrence Livermore National Laboratory under Contract No. W-7405-ENG-48.

Outline

• Review of earlier works

• Motivation

• Normal pointing uncertainty

• Pinhole image uncertainty

• Comparison of noise-based and new uncertainty

What causes the measurement uncertainty?

• Tolerances in the lenses

• Phase and amplitude aberrations of

wavefront

• Detector noises

• Noise introduced by optical defects

• Algorithm - Parameter variation

Uncertainty is an attempt to quantify these variations

Noise-based model uses Monte-Carlo simulation to estimate variations in position measurement

Original image Amplitude 50, noise 50

100 image sets are created for each noise level, the deviation of the position estimate is a measure of uncertainty

Position estimates from one set of 100 images

3 x the radial standard deviation is the measure of uncertainty

Uncertainty vs. noise curve generated from 800 images with varying amplitude and noise

Noise uncertainty with simulated KDP images

00.20.40.60.8

1

0 20 40 60

Noise level

Pixe

l unc

erta

inty

Amp. 200Amp. 100Amp. 50

These curves are part of a truth table associated with each algorithm. The truth table is looked up to find the uncertainty. The input to the table is an estimate of noise.

A generic algorithm is applied to all Automatic Alignment processing loops

Raw CCD Image

Image checkBlack/White

Off-normal processor

No

Algorithm

Position, uncertainty

YesOK

Off-normal detection

Position = f (x1,x2,x3..)

Position is a function of various parameters that are used by the algorithm, which are quantified by the uncertainty measurement

Various ROI lead to different position estimates

Centroid Positions from NPNT Algorithm383.688 208.505 1.50000

Centroid Positions from NPNT Algorithm 387.107 207.555 1.50000

Expanding or shrinking the ROI affects the position estimate (4 pixels variation shown)

Dynamic Thresholding example shows centroidlocation moves with different values

In the weighted centroid only the largest blob is chosen; a multimodal distribution could significantly vary the estimate

Distorted or asymmetric position variation

Somewhat Symmetric Asymmetric

As the profile changes between symmetric and unsymmetric, there is greater chance of position variability

Smaller portion remains after high threshold

Uncertainty is the range of centroid positions as threshold varies from minimum to ½ max (intensity)

Original image minTh = bkg + 3 * σ maxTh = ½ max(int)

Larger portion remains after low threshold

Uncertainty is the range of centroid positions obtained by adjusting the threshold

BEAM, LOOP = "TSF P4 FINE" (THRESHOLD) (NORMALIZE) 08-07-2006

242

242.2

242.4

242.6

242.8

243

243.2

243.4

243.6

256 256.5 257 257.5 258 258.5 259 259.5

X

Y

Range = 22 )min(max)min(max YYXX −+−

Lineout shows possible threshold range

Pinhole Image with Lineout

Threshold chosen to preserve shape of the object

Position estimate varies as threshold changes

Comparison of old and proposed method of uncertainty measurement

BEAM, LOOP = "AA TSF PINHOLE CHECK" UNCERTAINTY COMPARISON (8-8-06)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691 737 783 829 875 921 967 1013 1059 1105 1151

IMAGE INDEX

UN

CER

TAIN

TY (P

IXEL

S)

UNCERTAINTY (8-7-06) (M TH)UNCERTAINTY (8-1-06) (1 TH)UNCERTAINY (8-1-06) (NON-NORM)

This measurement results in higher uncertainty estimates

Comparison of old and proposed method of uncertainty measurement

REFERENCE, LOOP = "AA CSF P3 TSF P1" (ALGORITHM) UNCERTAINTY COMPARISON (8-8-06)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 500 1000 1500 2000 2500 3000

IMAGE INDEX

UN

CER

TAIN

TY (P

ixel

s)

UNCERTAINTY (8/7/06) (M Th)UNCERTAINTY (8-1-06) (1 Th)UNCERTAINTY (8-1-06) (non-Norm)

This measurement correlates well with image quality

Comparison of old and proposed method of uncertainty measurement

REFERENCE, LOOP = "AA ISP LM3 TSF P4" (ALGORITHM) UNCERTAINTY COMPARISON (8-8-06)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 110 219 328 437 546 655 764 873 982 1091 1200 1309 1418 1527 1636 1745 1854 1963 2072 2181 2290 2399 2508 2617

IMAGE INDEX

UN

CER

TAIN

TY (P

IXEL

S)

UNCERTAINTY (8-7-06) (M TH)UNCERTAINTY (8-1-06) (1 TH)UNCERTAINTY (8-1-06) (NON-NORM)

Normal Pointing Uncertainty Algorithm

REF MPAI CL Uncertainty (8-11-2006)

0

0.5

1

1.5

2

2.5

3

0 20 40 60 80 100 120 140

Index

Unc

erta

inty

(Pix

els)

Distribution shows how the uncertainty relates to the beam quality

When Normal Pointing Spot has multiple blobs

• Use a mask

• Calculate the weighted or binary centroid inside mask

Multimodal spot Multimodal spot Multimodal spot

Pinhole Uncertainty +/-2 Pixels from the Chosen Radius (8-16-2006)

0

0.5

1

1.5

2

2.5

3

3.5

4

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 121 127 133 139 145 151 157 163 169 175 181 187

Index

Unc

erta

inty

UNCERTAINTY Noise BaseUNCERTAINTY Radius Range

27

75

121

116

Pinhole uncertainty with +/-2 pixel rad variation

Pinhole Uncertainty +/-2 Pixels from the Chosen Radius (8-16-2006)

0

0.5

1

1.5

2

2.5

3

3.5

4

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 121 127 133 139 145 151 157 163 169 175 181 187

Index

Unc

erta

inty

UNCERTAINTY Noise BaseUNCERTAINTY Radius Range

27

75

121

116

#116

#27

#12127

Uncertainty measurement correlates well with image quality

Pinhole uncertainty with +/-2 pixel rad variation

Conclusion

• New algorithm shows more realistic uncertainty compared to noise-based value.

• Reference Images uncertainties are bounded between 0.2 and 0.4.

• Asymmetric or distorted beam caused by bad wave front have multiple blobs after segmentation and therefore higher uncertainty

Challenges

• Increase in processing time. Since the algorithm has to be executed multiple times (0.7 secs)

• Increase in uncertainty since it captures the position variations due to algorithm parameters