1. First-Order Opto-Mechanical Considerations in High Power Applications
Victor Villavicencio
NGIT / Defense Group
Technology Integration & Applications Operating Unit
Science and Engineering Applications
December 06

2. OUTLINE
Geometric versus Diffraction Limited Spot Diameter Approximations
Optical Element Parameters
Materials Properties
Thermal Effects/ Athermalization Approximations
Scattering Approximations
Software Tools

3. For M2 > 6, use (Geometric) Spot Diameter Approximations
RMS diameter
= 0.7 Dz/Fn
For Diffraction Limited System, Spot Diameter is defined as 86% of encircled energy
For Geometric System, Spot Diameter is defined as
“greater than 50% of encircled energy is within 70% of the marginal ray diameter”

4. Rules of Thumb for Opto-mechanical Tolerances
When Dealing with High Power first order Opto-Mechanical Calculations, need to first look thermal effects on Radius of Curvature, Lens Thickness, and scatter effects due to surface finish calculations. These values are shown with red values.

5. Thermal Effects on a Len Thickness and Radius of Curvature
In isotropic materials, a temperature change makes inside Dimensions scale as outside Dimensions. B’ A’ B A
A’ = DA + A
B’ = DB + B
DA = A a DT
DB = B a DT
Radius of Curvature, R, changes to
R’, using the same thermal expansion equation.

6. Use Superposition to Calculate stress due to temperature change
Thermal Stress, s
Use Superposition to Calculate stress due to temperature change
For Glass,
Do not exceed 1000 psi (7 MegaPascal)
in tensile stress
50,000 psi (350 MPa)
in compression stress

7. Thermo-Optic Coefficients, n, and CTE Values of Materials
n ( x 10-6/ Celsius)
Plastics thru –40
CTE is required to detemine Thermo-Optics Coefficients. Equation for defocus as a function of temperature on next slide.
CTE of Common Materials , a (x 10-6 /Celsius)
Aluminum 6061 / Brass
416 Stainless
Invar
Titanium
Glass to 7
Plastics – 80
Adhesives – 1000
Infrared Glasses thru 20

8. Thermal Effects
Singlets or Doublets or Triplets can be calculated as a single lens, for first order thermal effects defocus.

9. Total Integrated Scatter Measurement
TISb(s,l)
= s / ( s + r) = 1 – e –(4 p cosi/l) 
For a static surface at a constant temperature, the back scatter can be approximated by TISb.
Calculation for Straylight for 10W, 1.3 micron, 4% Fresnel Reflection:
( Powerreflected )* Eq. 1 = (10 * 0.04) * (4 Pi 0.08)^2 = Watts backwards scattered.

10. Back Scatter Approximation
The approximate backscatter
TIS is shown below:
TISb(s,l) =
This will be shown in the Plastic system example. Note scaling laws for wavelengths other than l are provided in references 1a and 1b.
Equations are normalized to the specularly reflected beam (not the incident beam), so TIS can be greater than 1.
As shown above, the approximate TIS is good for σ < ~λ/25.
That is, for s(l)/l > 0.04, the approximation underestimates the exact exponential form TIS.

11. U.S. Opto-mechanical design between various disciplines
Optics
Zernike
Analysis
Zemax
CodeV
ASAP
TracePro
4Sight
Vision
SigFit
Structures
NASTRAN
ANSYS
COSMOS
Other
Disciplines
Databases and
Translator Software
Fluid Mechanics
Acoustics
3D Graphics
CAD/CAM
AutoCAD
SolidWorks
ProEngineer
When first order calculations are not enough, need to use software packages as shown above.
For dynamic loads/vibration analysis – use Structures Softwares
For Circularly symmetric optics that needs to be transferred to CAD or Structures, use Zernikes polynomials
Control Systems
Heat Transfer
Sinda
TAP
MITAS
Matlab/Simulink
LabView/LabWindows

12. Conclusion References
Thermal effects and scattering first order calculations for high power applications.
In your experimental setup, use the incoherent rms spot size equation to determine spot size. This provides the largest (worst case) spot size.
TIS calculations are always conservative since it deals with surface roughness scatter. Internal straie /inclusions/stress will only slightly increase this TIS calculations.
To achieve geometrical approximations, thermal effects must be taken into account for plastics optics over DT = 20 C or more or glass optics needing to operate over DT= 40 C or more.
References
OPTI521 Class Notes, Fall, 2006.
Michael G. Dittman, Frank Grochocki, Kathleen Youngworth, No such thing as σ – flowdown and measurement of surface roughness requirements, Optical Systems Degradation, Contamination, and Stray Light: Effects, Measurements, and Control II, edited by O. Manuel Uy, Sharon A. Straka, John C. Fleming, Michael G. Dittman, SPIE Vol
Frank DeWitt IV, Georg Nadorff, Rigid Body Movements of Optical Elements due to Opto-Mechanical Factors Optical Modeling and Performance Predictions II, edited by Mark A. Kahan, SPIE Vol. 5867, (2005)

13. Back up Slides are slides 14 thru 17.

14. Diffraction Limited Approximations
Applies to M^2 < 4 Laser Systems
Minimum Spot
Diameter = l F/#
Depth of Focus = +/- 2 l (F/#)2
Zernike Polynomials don’t fit well under F-number of 1.5.
F/# is the “F-number”
Singlet

15. Various Mounting Techniques
a) Edge-mounted b) Surface-centered c) Cell-mounted
Sag
The z or “sag of a spherical surface” is calculated using the parabolic (k = -1) or circular ( k = 0) approximation. It has many uses. One use is determining lens edge thickness. Note ai is the Zernike coefficient and Zi is the Zernike Polynomial, which is only applicable for Circular pupils. R r
Sag z R

16. Calculating Tilt
Note f/D is the F# of the plano-convex lens
Figure 7 Accounting for tilt of a edge mounted element [3]
Using a semidiameter (SD) of 5 mm,
R = 162 mm and a gap of 0.7 mm , a tilt of 2 degrees was calculated.
This tilt value is used to determine effects on image quality using Zemax.

17. Calculating the Change in Focal Length for a Plastic Singlet, f = 25 mm, 10 mm diameter.
The focal length expands, due to the Dt = 40 C temperature rise, by
Df = -(n + ahousing) f DT
Where n is the plastic thermo-optics coefficient
, a is the CTE, f is the focal length, and DT is the temperature range.
From Table 2, 27 microns exceeds the 13 microns and therefore is outside the diffraction limits. Thus, the forward scatter calculation underestimates the scatter. Since the Wrms is > 0.04 l. adding actual surface roughness will only further increase the s value.
Table 2 – Plastic Singlet Dimensional
Changes due to 40 C temperature rise.
Note f/D is the F# of the plano-convex lens