OPTI 521 – Rules of Thumb CompilationGeometric Optics Name of rule: Ray deviation of plane parallel plateRule of thumb:

A tilted parallel plate causes a linear ray deviation, ∆ y=t ∙θ (n−1 )n

For glass at 45°, ∆ y= t3

When used: Light/rays incident on tilted windowWhy useful? Tilted windows are everywhere!Limitations: Beware small angle approximationRating:

Name of rule: Ray deviation angle of a small angle prism in airRule of thumb: The deviation angle of a small prism in air δ=α (n−1 )When used: Light/rays incident on wedged windowWhy useful? Wedged windows are everywhere!Limitations: Beware small angle approximationRating:

Name of rule: Image shift due to lateral motion of lensRule of thumb: Image shift due to lateral lens shift ∆ x i=∆ xl (1−m )When used: Quick lens tolerance analysisWhy useful? Easy to calculate lens sensitivity to transverse placement errorLimitations: Beware small angle approximationRating:

Name of rule: Image shift due to axial motion of lensRule of thumb: Image shift due to lateral lens shift ∆ zf=∆z l (1−m2 )When used: Quick lens tolerance analysisWhy useful? Easy to calculate lens sensitivity to axial placement errorLimitations: Beware small angle approximation, be careful with mirrorsRating:

Name of rule: Rotation Matrices for Small Angle PerturbationsRule of thumb:

R x=[1 0 00 cosα −sin α0 sinα cos α ]≅ [1 0 0

0 1 −α0 α 1 ]

R y=[ cos β 0 sin β0 1 0

−sin β 0 cos β ]≅ [ 1 0 β0 1 0

−β 0 1 ]R z=[cos γ −sin γ 0

sin γ cos γ 00 0 1]≅ [1 −γ 0

γ 1 00 0 1]

When used: Tracing rays with mirror angular perturbationsWhy useful? Easier to computeLimitations: Validity of small angle approximationRating:

Name of rule: Typical Effects of Prism RotationRule of thumb: For nearly all cases, prism rotation θ about the x, y, or z axis does one of:

1. causes image rotation about same axis by an amount 2θ2. has no effect on image about any axes3. causes image to rotate an amount + or - θ about the other two axes

When used: Determining effect of prism rotation on image/outputWhy useful? Sanity check – easy to make mistake in mirror matrix calculationsLimitations: Watch out for exceptions!Rating:

Optics ManufacturingName of rule: Machining Tolerances Guideline by Difficulty LevelRule of thumb: Coarse: ±1mm (±0.0040”)

Typical: ±0.25mm (±0.010”)Precision: ±0.025 (±0.001”)High Precision: < ±0.002mm (< ±0.0001”)

When used: When designing machine partsWhy useful? Helps to choose appropriate tolerances when designing partsLimitations: Depends on material, fab methods, equipment, supplier, etc.Rating:

Name of rule: Dimensional Tolerances Guidelines for Small LensesRule of thumb: Typical tolerances:

Diameter +0/-0.1mmThickness ±0.2mm

When used: Small optics (10-50mm)Why useful? Baseline for tolerancingLimitations: Depends on application – typical tolerances aren’t necessarily appropriateRating:

Name of rule: Wedge Tolerance GuidelineRule of thumb: Typical tolerances for wedge:

5 arcmin (easy)1 arcmin (readily achievable)15 arcsec (difficult, req. special care)

When used: Small optics (10-50mm)Why useful? Baseline for tolerancingLimitations: Depends on application – typical tolerances aren’t necessarily appropriateRating:

Name of rule: Bevel Size GuidelineRule of thumb: Typical bevel facewidths:⌀25mm: > 0.3mm⌀50mm: > 0.5mm⌀150mm: > 1mm⌀400mm: > 2mmWhen used: Designing lensesWhy useful? Appropriately sized bevels protect optical surfaces from chipsLimitations: Depends on application – typical bevel sizes aren’t necessarily appropriateRating:

Name of rule: Radius of Curvature Tolerance GuidelineRule of thumb: Typical tolerances:

R: ±0.2%Sag: ~3µm = 10 rings

When used: Designing and tolerancing lensesWhy useful? Point of reference for tolerancing lens performance in a systemLimitations: Depends on application – typical tolerances aren’t necessarily appropriateRating:

Name of rule: New Test Plate GuidelineRule of thumb: Test plate typical cost $1000, 2-3 wk lead timeWhen used: Designing lensesWhy useful? If the test plate you need isn’t available, this sets expectationsLimitations: Cost/lead time depends on material, size, type of surface, etcRating:

Rules of Thumb for Glass Properties ()

Parameter Base Precision High PrecisionRefractive index deviation from nominal ±0.001

(standard)±0.0005(grade 3)

±0.0002(grade 1)

Refractive index measurement ±3e-5(standard)

±1e-5(precision)

±0.5e-5(extra precision)

Dispersion deviation from nominal ±0.8%(standard)

±0.5%(grade 3)

±0.2%(grade 1)

Refractive index homogeneity ±1e-4(standard)

±5e-6(H2)

±1e-6(H4)

Stress birefringence(depends strongly on glass)

20nm/cm 10nm/cm 4nm/cm

Bubbles/inclusions (<50µm)(area of bubbles per 100cm3)

0.5mm2

(class B3)0.1mm2

(class B1)0.029mm2

(class B0)Striae (based on shadowgraph test) Normal quality

(has fine striae)Grade A(small striae in one direction)

Precision quality(none detectable)

Rules of Thumb for Lens Manufacture ()

Parameter Base Precision High PrecisionLens diameter 100µm 25µm 6µmLens thickness 200µm 50µm 10µmRadius of curvatureSurface sag

0.5%20µm

0.1%1.3µm

0.01% or 2µm0.5µm

Wedge (deviation of light) 5arcmin 1arcmin 15arcsecSurface irregularity 1 wave λ/4 λ/20Surface finish 50Å rms 20 Å rms 5 Å rmsScratch/dig 80/50 60/40 20/10Dimension tolerances, complex elements 200µm 50µm 10µmAngular tolerances, complex elements 6arcmin 1arcmin 15arcsecBevels (0.2-0.5mm typical) 0.2mm 0.1mm 0.02mm

Base: typical, no cost impact for loosening tolerances past these limitsPrecision: requires special attention, but readily achievable by most shops; ~25% cost premiumHigh Precision: Requires special equipment/personnel, ~100% cost premium

Tolerancing Optical DesignsName of rule: Lens ETD – Wedge Angle RelationsRule of thumb:

α=tan−1( ETDD )δ=α (n−1 ) cosθs=δ ∙ f

When used: Tolerancing lensesWhy useful? Links optical deviation to mechanical deviation for wedged surfaceLimitations: ETD measurement can be influenced by how lens is held, rotated, etc.Rating:

Name of rule: Mounting of Spherical Lenses/MirrorsRule of thumb: Wedge in spherical elements can be aligned out with proper optomechanical

design – use spherical surfaces as datumsWhen used: Designing opto-mechanical components to hold spherical elementsWhy useful? Can relax specification for wedge and achieve better performanceLimitations: This trick does not always work for aspherical elements, depends on how they

are specifiedRating:

Name of rule: Approximate Relation of Strehl Ratio to RMS Wavefront DistortionRule of thumb: SR=e−(2πω )2

When used: Converting between Strehl Ratio/RMS Wavefront Distortion for well-corrected systems

Why useful? Easy calculation

Limitations: Only valid for high SR/low wavefront distortion (ω≤ λ /4)Rating:

Name of rule: Relation of RMS Wavefront Distortion to Surface Figure ErrorRule of thumb: ΔW=Δ S (n−1 ) cosθWhen used: Evaluating impact of wavefront distortion/surface figure errorWhy useful? Result used oftenLimitations: n/aRating:

Name of rule: Relation of RMS Surface Roughness and ScatterRule of thumb: scatter=σ2 ,whereσ=2πωWhen used: Evaluating level of scatter caused by surface roughnessWhy useful? Estimating stray light/light lossLimitations: n/aRating:

Name of rule: Sag RelationsRule of thumb: sag≅ y2/2R=D2 /8 R; Δsag ≅−D2/8 R2

When used: Tolerancing lenses and opto-mechanicsWhy useful? Easy to remember and good approximation; exact solution is nasty algebraLimitations: Based on small-angle approximationRating:

CAD Modeling & FEAName of rule: Drawing a lens in SolidworksRule of thumb: Draw and dimension half cross-section, then revolve about axis to form lensWhen used: CAD modeling of optics/optical assembliesWhy useful? Many ways to draw a lens, but this is efficientLimitations: n/aRating:

Name of rule: Creating a lens assembly in SolidworksRule of thumb: Fix one object as reference; use concentric and coincident mates to constrain

parts together accordinglyWhen used: CAD modeling of optics/optical assembliesWhy useful? Many ways to build an assembly, but this is efficientLimitations: n/aRating:

Name of rule: Creating properly dimensioned drawings with hidden lines in SolidworksRule of thumb: Ensure "show hidden lines" is active before using Smart Dimension toolWhen used: CAD modeling of optics/opto-mechanical parts

Why useful? Easy to forget display of hidden lines on drawingLimitations: n/aRating:

Name of rule: Sanity-check your FEA resultsRule of thumb: FEA deformation and modal analysis calculations are highly sensitive to boundary

conditions, meshing, and myriad other factors. Double-check the FEA model output against handbook or hand calculations to prevent GIGO effect (garbage-in, garbage out).

When used: When carrying out FEA analysisWhy useful? FEA can easily spit out garbage resultsLimitations: NoneRating:

Name of rule: Solidworks FEA is convenient, but avoid if possibleRule of thumb: The built-in Solidworks FEA package is buggy and limited in functionality; avoid its

use if other more robust FEA packages are available (ANSYS, etc)When used: Desigining parts that will be placed under mechanical stressWhy useful? Save your sanity!Limitations: Commercial FEA packages are costly, may not be availableRating: (I wrote this one after struggling for hours with some weird errors)

Name of rule: Beware of boundary conditions when modeling kinematic constraints in FEARule of thumb: Mesh early, mesh often – sanity check the results before diving into detailed

mesh optimization, etc.When used: When modeling optics/mirror deformation in FEAWhy useful? Save time, save your sanityLimitations: It’s easy to get lost in the details when working with FEA simulationsRating:

Mechanical Properties of GlassName of rule: Stress-strain behavior of glassRule of thumb: Glasses do not deform plastically; deformations that do not result in rupture will

be elastic. The stress-strain curve is effectively linear to the rupture point. The modulus of elasticity for a typical glass is ~30Msi. The strength of glass is determined not by intrinsic material properties, but instead by the extent of defects/micro-fractures.

When used: When designing or building assemblies that put glass under stress/strainWhy useful? It helps to not shatter your expensive opticsLimitations: Depends on material; if approaching limits it’s best to check individual material

properties.Rating:

Name of rule: Determining effective stiffness of composite mechanical assembliesRule of thumb: Stiffness K adds for elements in parallel. Compliance C adds (K adds inversely) for

elements in series.When used: Deflection calculations, resonant frequency calculations, etc.Why useful? Can be used to build parametric models and determine effects of components on

the performance of the system as a wholeLimitations: Can be tricky to apply for elements with complicated geometries; this is when

FEA analysis software is useful.Rating:

Name of rule: Stress birefringenceRule of thumb: R=Ct (σ11−σ22 )

R: retardationC: stress optic coefficient (Brewster’s constant)t: thicknessσ 11 : first principal stressσ 22 : second principal stress

When used: When optics are mounted under stress (or have melt-induced stress)Why useful? Ties optical performance to opto-mechanical design; allows calculation of

OPD/aberrations due to stress.Limitations: n/aRating:

Name of rule: Value of the stress optic coefficientRule of thumb: The stress optic coefficient for glasses varies from 0-4 x 10-12/Pa, but many glasses

fall in the range of 2-3 x 10-12/Pa.When used: Calculating effects of stress birefringenceWhy useful? Allows estimation of OPD/aberrations due to stress in optical glassLimitations: Values for the stress optic coefficient are typically given at 589.3nm and 21°C, but

vary as a function of wavelength and temperature. Over the visible range this effect is small, but in IR/UV the stress optic coefficient should be verified.

Rating:

Stress, Strain, etc.Name of rule: Design parts for stiffnessRule of thumb: The stiffness of a beam is proportional to the cube of the thickness of the bent

dimension; it is linearly proportional to the thickness of the parallel dimension.When used: Designing parts that will be placed under mechanical stressWhy useful? Helps design parts that deflect less/have higher resonant frequenciesLimitations: Stiffness is only one variable in the tradeoffs done in mechanical designRating:

Name of rule: Increased stiffness of thin-layer adhesive bondsRule of thumb: The stiffness of a thin-layer adhesive bond is usually much greater than the

modulus of elasticity. The bulk modulus may be used instead to calculate stiffness.

When used: Deformation/dynamic analysis of assemblies containing thin adhesive bonds

Why useful? Stiffness of assemblies can be improved by choosing proper adhesive thicknessLimitations: Assumes the adhesive is much more compliant than the materials it is bonded toRating:

Name of rule: Condition for beam buckling under loadRule of thumb:

Pcrit=π2EIL2

(column)

Pcrit=4KL (pin joint with restoring force K)

When used: Determining buckling strength of components under compressionWhy useful? Buckling can be overlooked when designing a stressed assembly/componentLimitations: n/aRating:

AdhesivesName of rule: Mechanical properties of elastomeric bonds (rubber and RTV)Rule of thumb: Shear modulus G: ~100 psi (~1 MPa)

Young's modulus E0: ~3G = 300 psi (~3 MPa)Bulk modulus EB: ~100000 psi (~1000 MPa)Shear stiffness Ks = dFshear/dy = GA/t (very compliant)Axial stiffness K1 = dFaxial/dz = E0A/L (very compliant)Compressive stiffness K2 = dFaxial/dz = EBA/T (thin, constrained; very stiff)

When used: Quick calculations/estimates for elastomeric bondingWhy useful? Calculating deflections, bond strength, resonant frequencies, etcLimitations: General case, ignores shape change effects. Materials will have properties varying

from these guidelines so when it matters obtain/determine actual material parameters.

Rating:

Name of rule: Axial stiffness and shape factor for elastomeric bondsRule of thumb: Axial stiffness KZ = dFaxial/dz = ECA/t,

Compression modulus EC = E0 (1+φS2),Shape factor S = Aload/Abulge

When used: Calculating deflections, etc for general geometry elastomeric bondsWhy useful? Will provide better estimate than using more general guidelines aboveLimitations: For large values of S, EC blows up; use EB as maximum value for EC

Rating:

Thermal DistortionName of rule: Thermally induced shear stress on a thin adhesive bondRule of thumb: τ epoxy=

Ga ΔT2 t (α 1−α 2 )

G: shear modulus of epoxya: max dimension of bond (diameter, length)

t: thickness of bondΔT: temperature changeα1, α2: bonded materials' coefficients of thermal expansion

When used: When using adhesives to bond dissimilar materialsWhy useful? Can use to determine approximate safety factor for adhesive bond under

temperature excursionsLimitations: Neglects bending of bonded area; assumes adhesive is fully compliantRating:

Name of rule: Shear strain in mismatched, bonded materials under thermal stressRule of thumb: Maximum shear strain γ at distance a/2 from center:

γ= a2 t (α1−α2 ) ∆T

Shear stress τ at distance a/2 from center:

τ=Gγ=Ga2 t (α 1−α 2 )∆T

For thick substrates (a/t < 100),substrate complianceadhesive compliance

≅ 0.1 at

Gepoxy

E substrate,

Gepoxy ~150 ksiWhen used: Estimating strain, survivability in bonds under thermal stressWhy useful? Easy calculation to check if your bond will survive shipping, operating conditions,

etcLimitations: Conservative estimate, ignores compliance of substratesRating:

Name of rule: Bending of a beam by thermal gradientsRule of thumb: A thermal gradient across a beam will cause it to bend in an arc, according to:

∆θ∆ L

= 1R

=α ∂T∂ y

When used: Non-uniform heating of beam elementsWhy useful? Determine deflection or stressLimitations: Does not handle more complicated geometry or thermal distributionRating:

Name of rule: Thermal bending of a beam with CTE gradientRule of thumb: When heated or cooled, a beam with non-uniform CTE thermal will bend in an

arc, according to: ∆θ∆ L

= 1R

=∂ (αT )∂ y

When used: Heating/cooling of beam elements with non-uniform CTEWhy useful? Determine deflection or stressLimitations: Does not handle more complicated geometry or CTE distributionRating:

Shock & Vibration IsolationName of rule: Transmissibility for a vibration-isolated systemRule of thumb:

T= isolatedmotionbasemotion

=√ 1+(2 ωωn

CR)2

(1− ω2

ωn2 )2

+(2 ωωn

C R)2

ω: frequency of isolated systemωn: frequency of base (isolator) systemCR: system damping factor

When used: Estimating performance of a vibration-isolated systemWhy useful? Useful in estimating jitter, etcLimitations: Need to know quantities ω, ωn, CR which for a complicated system/assembly may

not be straightforward; will give incorrect results when resonance peaks are close/overlap

Rating:

Name of rule: Miles equationRule of thumb:

arms=√ π2

f nQ PSDISO

fn: object's natural frequencyQ: resonance amplification factorPSDISO: PSD driving oscillation of damped system (in g2/Hz)arms: acceleration (in g)

δ rms=gT ( f n )√ π32π3

Qf n3 PSDBASE

g: acceleration of gravityT(fn): transmissibilityPSDBASE: PSD driving oscillation acting on dampers (in g2/Hz)δrms: displacement

When used: Estimating acceleration and displacement amplitudes of an isolated systemWhy useful? Useful in estimating jitter, etcLimitations: Need to know quantities fn, Q, PSDISO which for a complicated system/assembly

may not be straightforward; will give incorrect results when resonance peaks are close/overlap

Rating:

Name of rule: Shock loading estimationsRule of thumb: Simple handling results in 3g shocks

Peak acceleration for object dropped from height h:

Ag=√ hδ sw

Ag: peak acceleration in g

h: drop heightδsw: self-weight displacement

When used: Estimating peak accelerations during handling, shipping, launching, etcWhy useful? Gain insight as to whether a system will break during handling, etcLimitations: Ignores rotational energy, internal stresses when object is suddenly acceleratedRating:

Flexures, Actuators, and Motion ControlName of rule: The reduced tensile modulus figure of merit for flexure materialRule of thumb: Yield / E is a figure of merit for a flexure material (higher value indicates a better

flexure material)When used: Determining materials used in flexuresWhy useful? Helps with trade studies when designing with flexuresLimitations: Does not take into account other factors – specific requirements, cost, etcRating:

Name of rule: Flexure complexity vs. performanceRule of thumb: Simple flexures do not perfectly constrain motion, they have cross-talk; more

complicated geometry flexures can reduce or eliminate the cross-talk motionWhen used: Designing flexuresWhy useful? Be aware of cross-talk when designing and adjust flexure complexity based on

requirementsLimitations: Flexures are not always the best solutionRating:

Name of rule: Displacement of ceramic/piezo materialRule of thumb: ΔLj = Sj L0 = dij Ei L0,

ΔLj displacementSj mechanical strain in direction j (dimensionless)L0 material thickness in field direction (m)dij piezoelectric deformation coefficienct (pm/V)Ei electric field along direction iCommonly used stack actuators achieve a deformation of 0.2%

http://www.piceramic.com/piezo_tutorial4.php

When used: Determining stroke of piezo actuatorsWhy useful? Can help to determine size/drive requirements for piezo actuatorsLimitations: Do not exceed piezo material electric field breakdown thresholds ~1-2 kV/mmRating:

Mounting DistortionName of rule: Round mirror self-weight deflection, horizontal mountingRule of thumb: Theoretical self-weight deflection with 3pt edge support, horizontal

orientation:

δ ≅ C sp( ρgE ) r4

h2 (1−υ2 )δ: mirror deflection

Csp: geometric support constant; for a 3-point equal-spaced edge support Csp = 1.356g: acceleration of gravityρ/E: inverse specific stiffness (density ρ, elastic modulus E)υ: Poisson’s ratio

When used: When estimating surface figure errors with mirrors mounted horizontallyWhy useful? 1) Easy calculation to estimate surface figure/wavefront distortion errors

induced by mounting2) Nice way to compare different mounting strategies

Limitations: This is an approximation; mirrors with varied geometry (strong curvature, asymmetry, etc) will depart from this approximation. Not a bulletproof substitute for FEA analysis.

Rating:

Name of rule: Round mirror self-weight deflection, vertical mountingRule of thumb: Theoretical self-weight deflection with 3pt edge support, vertical orientation:

δHrms≅ (a0+a1 γ+a2 γ2)( 2ρgE )r2 ,γ=( r2

2hR )δ: mirror deflection

g: acceleration of gravityρ/E: inverse specific stiffness (density ρ, elastic modulus E)R: mirror radius of curvatureFor a two point support, a0 = 0.5466, a1 = 0.2786, a2 = 0.110For a flat mirror, γ = 0 (R = ∞)

When used: When estimating surface figure errors with mirrors mounted verticallyWhy useful? 1) Easy calculation to estimate surface figure/wavefront distortion errors

induced by mounting2) Nice way to compare different mounting strategies

Limitations: This is an approximation; mirrors with varied geometry (strong curvature, asymmetry, etc) will depart from this approximation. Not a bulletproof substitute for FEA analysis.

Rating:

Properties of Common Optical Materials()

BK7The good: Good optical performance, cheap, readily available, very commonThe bad: Cuts out in DUV and NIRWavelength range: 320nm – 2300nmRefractive index: nd: 1.51680Abbe number: vd: 64.17Density: 2.51 g/cm3Modulus of elasticity: 82 GPaCTE: 7.1 ppm/K @ -30/+70CThermal conductivity: 1.114 W/m/KNotable application: Cost-effective optics

Fused Silica SiO2The good: Very low CTE, depending on grade/type can have excellent transmission in DUV (e.g. Lithosil)

or NIR (e.g. Infrasil)The bad: Transmission in IR/DUV highly dependent on melt impurities/grade; watch out for

fluorescence in UV applications. Relatively high dn/dt, ~10 ppm/C.Wavelength range: 170nm – 2230nm (Lithosil), 250nm – 3500nm (Infrasil)Refractive index: nd: 1.45843Abbe number: vd: 67.83Density: 2.20 g/cm3Modulus of elasticity: 73 GPaCTE: 0.52 ppm/K @ -30/+70CThermal conductivity: 1.30 W/m/KNotable application: ArF (193nm) lithography projection optics; resists thermal shock

Calcium Fluoride CaF2The good: Very wide transmission band from VUV to MIRThe bad: Fragile, expensive; UV transmission highly dependent on gradeWavelength range: 130nm – 10µmRefractive index: nd: 1.43384Abbe number: vd: 95.23Density: 3.18 g/cm3Modulus of elasticity: 76 GPaCTE: 18.41 ppm/K @ -30/+70CThermal conductivity: 9.71 W/m/KNotable application: ArF (193nm) lithography projection optics, broadband transmitting windows

P-PK53The good: Low Tg, good for moldingThe bad: Terrible transmission in UVWavelength range: 365nm – 1970nmRefractive index: nd: 1.52690Abbe number: vd: 66.22Density: 2.83 g/cm3Modulus of elasticity: 59 GPaCTE: 13.3 ppm/K @ -30/+70CThermal conductivity: 0.640 W/m/K

Notable application: Precision molded optics

Acrylic (PMMA)The good: Good transmission in visible, well suited for injection molding (cheap in mass quantities)The bad: Intolerant of high temperatures, poor UV and IR transmission, poor thermal propertiesWavelength range: 360nm – 1150nmRefractive index: nd: 1.4914Abbe number: vd: 52.60Density: 1.18 g/cm3Modulus of elasticity: 3.3 GPaCTE: 50-100 ppm/KThermal conductivity: 0.050 W/m/KNotable application: Precision molded optics, used in photoresists

Sapphire Al2O3The good: Transmits deep into UV; very hard material; resists scratching, pressure, thermal shock; high

refractive index; excellent chemical resistanceThe bad: Slightly birefringent, difficult to polish, expensiveWavelength range: 150nm – 5.5µmRefractive index: nd: no 1.76817, ne 1.76009Abbe number: vd: vo 72.31, ve 72.99Density: 3.97 g/cm3Modulus of elasticity: 335 GPaCTE: 5.6 ppm/K (para), 5.0 ppm/K (perp)Thermal conductivity: 27.21 W/m/KNotable application: Wide bandwidth windows, durable optics (eg. watch glass), efficient ball lenses (fiber

coupling)

Zinc Selenide ZnSeThe good: Excellent transmission from visible (yellow) into MIR; very high refractive index; low

absorptionThe bad: Expensive; substrate thickness limited to ~30mm by CVD process; highly toxic dust (forms

hydrogen selenide when ingested); does not transmit shorter wavelength visible (green and beyond); high Fresnel losses without AR coating

Wavelength range: 600nm – 16µmRefractive index: 2.4028 @ 10.6µmAbbe number: vd: 84.45Density: 5.27 g/cm3Modulus of elasticity: 70 GPaCTE: 7.1 ppm/KThermal conductivity: 18.0 W/m/KNotable application: Favored for high power IR laser optics (Nd:YAG, CO2, etc), especially when some visible

transmission required

Zinc Sulfide ZnSThe good: Standard grade is relatively cheap compared to ZnSe; multi-spectral grade offers good

transmission from VIS to MIR (otherwise VIS T very low); very high refractive index; hard and tough material

The bad: Substrate thickness limited to ~30mm by CVD process; high Fresnel losses without AR coating, does not transmit in visible (~0% T @ 500nm); multi-spectral grade is expensive; dust is toxic (forms H2S when ingested)

Wavelength range: 370nm – 13.5nm (multi-spectral), 2µm – 14µm (laser grade CVD)Refractive index: 2.20084 @ 10µmAbbe number: vd: ~19.9Density: 4.09 g/cm3Modulus of elasticity: 85.5 GPaCTE: 6.5 ppm/KThermal conductivity: 27 W/m/KNotable application: Standard ZnS: Lower-cost MIR laser optics (Nd:YAG, CO2, etc) when no visible transmission is

requiredMulti-Spectral ZnS: For applications requiring VIS through MIR transmission

Germanium GeThe good: Good thermal conductivity, good strength and hardness; useful in MIRThe bad: Extremely high dn/dt (408 ppm/K) and runaway thermal absorption; not suitable for high

power IR laser optics, high Fresnel losses without AR coatingWavelength range: 2µm – 12µmRefractive index: 4.0031 @ 10µmAbbe number: n/aDensity: 5.32 g/cm3Modulus of elasticity: 100 GPaCTE: 5.7 ppm/KThermal conductivity: 59 W/m/KNotable application: Imaging optics for 2-12µm spectral region

Magnesium Fluoride MgF2The good: Transmission from VUV to MIR (7µm), low refractive indexThe bad: Slightly birefringent; painfully expensiveWavelength range: 120nm – 7µmRefractive index: d: no 1.37774, ne 1.38956Abbe number: d: vo 106.22, ve 104.86Density: 3.18 g/cm3Modulus of elasticity: 138 GPaCTE: 13.7 ppm/K (para), 8.9 ppm/K (perp)Thermal conductivity: 21 W/m/K (para), 33.6 W/m/K (perp)Notable application: Widely used as broadband AR coating material; employed in UV optics and excimer lasers

Properties of Common Structural Materials()

Steel, 1010 mildThe good: Good machinability, weldability, formability; relatively inexpensiveThe bad: Relatively weak steel alloyDensity: 7.8 g/cm3Modulus of elasticity: 200 GPaCTE: 12.2 ppm/KThermal conductivity: 49.8 W/m/KNotable application: Cold headed fasteners

Stainless steel, 17-4 CRESThe good: High strength, good corrosion resistance, good mechanical propertiesThe bad: Difficult to machine and weldDensity: 7.8 g/cm3Modulus of elasticity: 197 GPaCTE: 12.2 ppm/KThermal conductivity: 49.8 W/m/KNotable application: Nuclear waste casks, food industry, aerospace (turbine blades, etc)

Aluminum, 6061-T6The good: Good machinability, weldability, formability, thermal conductivity, electrical conductivity;

cheapThe bad: High CTEDensity: 2.7 g/cm3Modulus of elasticity: 68.9 GPaCTE: 23.6 ppm/KThermal conductivity: 167 W/m/KNotable application: General all-purpose aluminum alloy

Aluminum, 7075-T6The good: Super high strength Al alloyThe bad: High CTEDensity: 2.81 g/cm3Modulus of elasticity: 71.7 GPaCTE: 23.6 ppm/KThermal conductivity: 130 W/m/KNotable application: Aircraft fittings

Aluminum, 5083-H321The good: Highest strength of non-heat treable Al alloys, excellent corrosion resistanceThe bad: High CTEDensity: 2.66 g/cm3Modulus of elasticity: 70.3 GPaCTE: 23.8 ppm/KThermal conductivity: 117 W/m/KNotable application: Boat hulls

BerylliumThe good: High ductility, stiffness-to-weight ratio, thermal conductivityThe bad: Soft, brittleDensity: 1.84 g/cm3Modulus of elasticity: 303 GPaCTE: 11.5 ppm/KThermal conductivity: 216 W/m/KNotable application: X-ray tube windows, lightweight structural components, satellite mirrors

TitaniumThe good: Highest strength-to-weight ratio of any metal, ductile, corrosion resistanceThe bad: Expensive, difficult to machine, poor thermal conductivityDensity: 4.51 g/cm3Modulus of elasticity: 116 GPaCTE: 8.6 ppm/KThermal conductivity: 21.9 W/m/KNotable application: Used in medical implants, bone fracture repair, flexures

CopperThe good: Excellent thermal and electrical conductivity, ductileThe bad: Soft metal, heavyDensity: 8.96 g/cm3Modulus of elasticity: 110-128 GPaCTE: 16.5 ppm/KThermal conductivity: 401 W/m/KNotable application: Mirrors in high-power CO2 laser delivery systems, electrical wire, heat sinks

Invar 36The good: Excellent thermal stability (near zero CTE)The bad: Difficult to machine, expensive, heavy, tendency to creep over time; expensiveDensity: 8.05 g/cm3Modulus of elasticity: 141 GPaCTE: 0.6-1.2 ppm/KThermal conductivity: 10 W/m/KNotable application: Mirrors in high-power CO2 laser delivery systems, electrical wire, heat sinks

Graphite epoxy (CFRP)The good: Very strong and lightThe bad: Expensive, must be custom molded for applicationDensity: 1.60 g/cm3Modulus of elasticity: 70 GPaCTE: ~1 ppm/KThermal conductivity: W/m/KNotable application: Frames on race vehicles

Silicon CarbideThe good: Extremely hard; high stiffness to mass, low CTEThe bad: Sintering process is difficultDensity: 3.21 g/cm3

Modulus of elasticity: 450 GPaCTE: 2.77 ppm/KThermal conductivity: 3.6-4.9 W/m/KNotable application: Grinding tools, lightweight mirrors

MagnesiumThe good: Strong, lightweightThe bad: Flammable, corrosionDensity: 1.74 g/cm3Modulus of elasticity: 45 GPaCTE: 24.8 ppm/KThermal conductivity: 156 W/m/KNotable application: Lightweight racing wheels, aerospace, mobile/portable electronics (cases)

TeflonThe good: Chemical resistance (inert), low frictionThe bad: Soft, flows over timeDensity: 2.16 g/cm3Modulus of elasticity: 0.55 GPaCTE: 75 ppm/KThermal conductivity: 0.25 W/m/KNotable application: Non-stick frying pans

Solid Mechanics Summary()

Normal Stress and StrainNormal stress σ results from axial loads on a member (perpendicular to the cross section). The average normal stress is determined by the ratio of internal force to cross sectional area:

σ avg=forcearea

= PA

Normal stress may be compressive or tensile; by definition tensile stresses are positive and compressive stresses are negative.The units of normal stress are the same as for pressure:

psiPa = N/m2

MPa = N/mm2

1 psi ≈ 7000 Pa

Normal strain ε is the normalized elongation caused by a normal stress, defined as ¿ ΔLL ,

where ΔL is the change in length due to strain and L is the unstrained length. Normal strain is a dimensionless quantity.For small deflections in homogeneous material, the normal strain is proportional to the normal stress: εE=σ, where E is Young’s modulus or the modulus of elasticity. Young’s modulus has units equivalent to pressure.

Shear Stress and StrainShear stress τ results from parallel loads on a member spread over an area. It is defined as τ=V

A , where V is shear force and the A is the area over which force is applied. The units of shear stress are equivalent to pressure.Shear strain γ is the angular deformation of a shape resulting from a shear stress, defined as γ= τ

G , where G is the shear modulus or modulus of rigidity. Shear strain is a dimensionless quantity (radians); the shear modulus has units equivalent to pressure.Poisson Ratio

The Poisson ratio ν is defined as the negative of the ratio of transverse strain ε z to axial strain ε x:

ε z=Δ LL

ε x=Δww

ν=−ε z

εx

Bulk ModulusThe bulk modulus is a material property that indicates compressibility. It is defined as EB=

−PΔV /V for an element in uniform hydrostatic pressure P with normalized volume

change ΔV/V.The bulk modulus is related to Young’s modulus and also to the shear modulus. For isotropic materials, EB=

E3 (1−2ν ) . For linear isotropic materials, G= E

2 (1+ν ) .

Strain-Stress Curve for a Typical Metal

Image taken from http://en.wikipedia.org/wiki/Deformation_(engineering)

Yield Strength and Precision Elastic Limit

Yield strength σ YS is defined as the maximum stress a material can withstand without undergoing plastic deformation. For materials without a clear yield point in the strain-stress curve, yield strength is typically defined as the stress that results in 0.2% permanent strain.The precision elastic limit σ PEL, or micro-yield strength, is defined as the stress that results in 0.0001% (1 ppm) permanent strain.

GD&T Symbols Quick Reference()

Fastener Thread & Tap Drill Reference()

American Standard Thread Size ISO Metric Thread SizeThread Tap Drill Thread Tap Drill

(in.) (mm)0-80 3/64 M1 x 0.25 0.751-64 53 M1.1 x 0.25 0.851-72 53 M1.2 x 0.25 0.952-56 51 M1.4 x 0.3 1.102-64 50 M1.6 x 0.35 1.253-48 5/64 M1.8 x 0.35 1.453-56 46 M2 x 0.4 1.604-40 43 M2.2 x 0.45 1.754-48 42 M2.5 x 0.45 2.055-40 39 M3 x 0.5 2.505-44 37 M3.5 x 0.6 2.906-32 36 M4 x 0.7 3.306-40 33 M4.5 x 0.75 3.708-32 29 M5 x 0.8 4.208-36 29 M6 x 1 5.00

10-24 25 M7 x 1 6.0010-32 21 M8 x 1.25 6.8012-24 17 M9 x 1.25 7.8012-28 15 M10 x 1.5 8.501/4-20 7 M11 x 1.5 9.501/4-28 3 M12 x 1.75 10.20

5/16-18 F M14 x 2 12.005/16-24 I M16 x 2 14.003/8-16 5/16 M18 x 2.5 15.503/8-24 Q M20 x 2.5 17.50

7/16-14 U M22 x 2.5 19.50

7/16-20 W M24 x 3 21.001/2-13 27/64 M27 x 3 24.001/2-20 29/64 M30 x 3.5 26.50

9/16-12 31/64 M33 x 3.5 29.509/16-18 33/64 M36 x 4 32.005/8-11 17/32 M39 x 4 35.005/8-18 37/64 M42 x 4.5 37.503/4-10 21/32 M45 x 4.5 40.503/4-16 11/16 M48 x 5 43.007/8-9 49/64 M52 x 5 47.00

7/8-14 13/16 M56 x 5.5 50.501"-8 7/8 M60 x 5.5 54.50

1"-14 15/16 M64 x 6 58.00M68 x 6 62.00