## Use of thermal sieve to allow optical testing of cryogenic optical systems |

Optics Express, Vol. 20, Issue 11, pp. 12378-12392 (2012)

http://dx.doi.org/10.1364/OE.20.012378

Acrobat PDF (1625 KB)

### Abstract

Full aperture testing of large cryogenic optical systems has been impractical due to the difficulty of operating a large collimator at cryogenic temperatures. The Thermal Sieve solves this problem by acting as a thermal barrier between an ambient temperature collimator and the cryogenic system under test. The Thermal Sieve uses a set of thermally controlled baffles with array of holes that are lined up to pass the light from the collimator without degrading the wavefront, while attenuating the thermal background by nearly 4 orders of magnitude. This paper provides the theory behind the Thermal Sieve system, evaluates the optimization for its optical and thermal performance, and presents the design and analysis for a specific system.

© 2012 OSA

## 1. Introduction

1. M. Clampin, “Status of the James Webb Space Telescope (JWST),” Proc. SPIE **7010**, 70100L, 70100L-7 (2008). [CrossRef]

1. M. Clampin, “Status of the James Webb Space Telescope (JWST),” Proc. SPIE **7010**, 70100L, 70100L-7 (2008). [CrossRef]

2. D. M. Chaney, J. B. Hadaway, J. Lewis, B. Gallagher, and B. Brown, “Cryogenic performance of the JWST primary mirror segment engineering development unit,” Proc. SPIE **8150**, 815008, 815008-12 (2011). [CrossRef]

*i.e.*no direct contact) from any heat sources. iii) Radiation: Thermal radiation from a hot object needs to be blocked before it reaches to the optical system.

*e.g.*~35K) temperature may cost a significant portion of the total project budget. Thus, it is highly desired to use an existing collimator such as LOTIS operating at an ambient temperature (

*e.g.*~300K) [3

3. S. C. West, S. H. Bailey, J. H. Burge, B. Cuerden, J. Hagen, H. M. Martin, and M. T. Tuell, “Wavefront control of the Large Optics Test and Integration Site (LOTIS) 6.5m collimator,” Appl. Opt. **49**(18), 3522–3537 (2010). [CrossRef] [PubMed]

## 2. Cryogenic optical testing using Thermal Sieve

### 2.1 Optical testing configuration using TS

*N*: Number of thermal plates, ii)

*S*: Spacing between the thermal plates, iii)

*D*: hole diameter, and iv)

_{hole}*I*: Interval between holes.

*i.e.*propagation angle) of the test beam to a spatial light distribution at the focal plane. Different diffraction orders at the focal plane represent the Point Spread Function (PSF) of the system for different field angles. By evaluating the zero order (

*i.e.*on-axis) PSF only, various optical testings (

*e.g.*wavefront measurement, point source imaging) can be made downstream [5

5. S. B. Hutchison, A. Cochrane, S. McCord, and R. Bell, “Update status and capabilities for the LOTIS 6.5 meter collimator,” Proc. SPIE **7106**, 710618, 710618-12 (2008). [CrossRef]

### 2.2 Thermal transfer control using TS

*T*and

_{H}*T*. (For more accurate calculations, these spaces may be modeled including the actual collimator and optical system with reflecting and radiating surfaces.) As an example configuration, three thermal plates were set as graybodies with controlled temperatures

_{C}*T*and emissivity

_{1-3}*ε*values. The emissive power

_{1-3}*J*from these graybodies is given from Stefan-Boltzmann lawwhere

*ε*is the emissivity,

*σ*is the Stefan-Boltzmann constant 5.67x10

^{−8}

*W/m*, and

^{2}/K^{4}*T*is the absolute temperature of the graybody.

*J*should be equal to the sum of the four emissive power components depicted as dotted arrows in Fig. 2. Then, the thermal transfer equation becomes

_{net_2-}*α*of each thermal plate was defined as the ratio of the not-a-hole region area to the whole thermal plate area. Two effective solid angle Ω

*and Ω*

_{eff1}*represent the sum of solid angles encompassed by the array of holes in the neighboring plate (*

_{eff2}*S*away) and the following plate (2

*S*away), respectively. These solid angles are expressed using approximated projected solid angles with

*cos*scale factor asandwhere

^{4}θ*θ*is the angle shown in Fig. 3 . The

*n*and

*m*represent the relative column and row differences between two holes in the thermal plates as depicted in Fig. 3. Infinite number of holes (i.e. infinite

*n*and

*m*) was assumed instead of using the actual number of the holes. This eliminates the geometrical asymmetry problem (e.g. edge effect) for evaluating the effective solid angles not at the center of thermal plate. Fortunately, due to the rapid drop of

*cos*, this assumption hardly affects the evaluated solid angle values.

^{4}θ## 3. Thermal Sieve design considerations

### 3.1 Independence between hole-sets

*N*holes aligned along the optical axis as the test beam passes through the

*N*thermal plates in Fig. 1 (right), is a numerically demanding simulation due to the interaction among the complex light fields from the thousands of hole-sets. Especially, the periodic pattern needs to be perturbed to model imperfect alignment, and it becomes almost an impossible simulation task within today’s computing power.

*I*needs to be larger than the extent of diffraction spread in the geometrical shadow region (

*i.e.*outside a hole). Then, most of the light can go straight through a hole-set without interacting with other holes. In other words, the diffraction spread needs to be small compared to the hole size

*D*and the interval

_{hole}*I*between the holes. (Note:

*I*>

*D*by definition shown in Fig. 1.) Using the edge diffraction model [6], which approximates the spread from the circular aperture edge, a condition for

_{hole}*D*defined in terms of wavelength

_{hole}*λ*and propagation distance

*S*asA scale factor of 2 was applied to take account the spread in both directions, and the extent of the spread was chosen where the irradiance drops down to <~5% of the nominal irradiance from the edge diffraction model [6].

*A*is the amplitude,

*Φ*is the phase in waves,

*λ*is the wavelength of the field. The actual field is the real part of this complex field. Based on the Fresnel near-field diffraction model [7] the complex field at the next thermal plate

*U*becomeswhere

_{n}(x_{n}, y_{n})*FF*represents the 2D Fourier transform,

*U*is the complex field at the previous thermal plate, and

_{p}(x_{p}, y_{p})*S*is the distance between thermal plates (

*i.e.*propagation distance).

*i.e.*squared modulus of the complex field) at each holes are presented in Fig. 4 .

### 3.2 Separation of multiple diffraction orders

*f*for this discussion. This is a valid approximation since the location of different diffraction orders depends only on the focal length

_{eff}*f*. (Of course, the specific shape of the complex field still depends on the physical properties of the actual system such as aperture shape and size.)

_{eff}*U*is expressed in a 2D Fourier transform of the test beam complex field

_{focal}*U*aswhere

_{TS}*f*is the effective focal length of the optical system under test. The complex field

_{eff}*U*is the complex field after passing through the TS, and can be expressed aswhere ** represents the 2D convolution,

_{TS}*I*is the interval between holes,

*D*is the diameter of the TS circular aperture, and

_{TS}*U*is the complex field in a hole at the last thermal plate. Identical complex field

_{hole}*U*was assumed for all holes at the last thermal plate thanks to the independence assumption in Section 3.1, so that

_{hole}*U*was expressed using 2D

_{TS}*comb*function defined in Appendix A.1.

*somb*(defined in Appendix A.1) and the modulated

*comb*function. The intensity distribution

*Q*of the

*somb*function is the well-known Airy disk pattern in Eq. (11).

*D*is defined as the diameter of the first minimum intensity circle asand shown in Fig. 6 (left). Another part of

_{Airy}*U*in Eq. (10) is the modulated

_{focal}*comb*function. The relative amplitude and phase factor for each delta function in the comb function depends on the Fourier transform of

*U*. However, the spatial locations of those delta functions are defined simply by the interval

_{hole}*K*given asfor the effective focal length

*f*, wavelength

_{eff}*λ*and the interval between holes

*I*.

*U*in Eq. (10) becomes an array of many Airy disk patterns spaced by

_{focal}*K*. The first nine diffraction orders from (−1, −1) to (1, 1) order are shown in Fig. 6 (right). These diffraction orders, for a small

*K*, may overlap to each other. However, if

*K*is large enough compared to the size of the Airy disk

*D*, the orders can be separated from each other without overlapping. Also, for a typical testing configuration, the limiting aperture may be the optical system under test, not the TS. It means that the Airy disk size in Eq. (12) will depend on the diameter of the optical system aperture

_{Airy}*D*instead of

_{system}*D*.

_{TS}*λ*, effective focal length

*f*, and the system aperture diameter

_{eff}*D*. By re-writing Eq. (14) the interval

_{system}*I*between holes needs to satisfyas a condition for the diffraction order separation.

## 4. Thermal Sieve performance demonstration

### 4.1 Thermal performance of TS

*ε*, absolute temperature of the thermal plates

_{1-3}*T*, temperature of the hot collimator space

_{1-3}*T*, temperature of the cold optical system space

_{H}*T*, and the obscuration ratio of the thermal plate

_{C}*α*. The effective solid angle Ω

*and Ω*

_{eff1}*were given in Eq. (3) and (4).*

_{eff2}*J*values are determined. The thermal loads to the optical system space

*ΔJ*and the collimator space

_{C}*ΔJ*are given as where

_{H}*J*and

_{net_1 ±}*J*are depicted in Fig. 2. A positive thermal load means incoming thermal energy to the space, and a negative value means outgoing thermal energy from the space. The magnitude of these thermal loads needs to be minimized, so that thermal gradients on the optical systems are minimized during the cryogenic testing.

_{net_4 ±}*ΔJ*were plotted as a function of the spacing

_{C}*S*between thermal plates. The Zemax simulation results were shown in blue dots and the analytical calculations using Eq. (16) were plotted in red curve. They match well with each other except for very small

*S*values, where the solid angle approximation in Eq. (3) and (4) is no longer valid as the spacing

*S*approaches zero. Since the approximated solid angle is larger than the exact value (e.g. The approximated solid angle goes to infinity as

*S*approaches zero.), Zemax simulation shows less thermal loads for the small spacing values

*S*<~0.005m in Fig. 7 . However, this discrepancy only happens for very small

*S*values, which is impractical to be manufactured anyway.

*T*and

_{1}*T*were fixed at the same temperatures as the collimator space temperature and the optical system space temperature, respectively. The second plate’s temperature

_{3}*T*was varied from 150

_{2}*K*to 300

*K*.

*ΔJ*and

_{C}*ΔJ*for nine different emissivity combinations were calculated and plotted in Fig. 8 . For the 1st and 3rd plate, the higher emissivity values showed better thermal performance. In other words, more blackbody-like plate makes the thermal loads closer to 0. The 2nd plate’s emissivity

_{H}*ε*turned out to be an effective parameter to reduce the thermal loads. For instance, by decreasing

_{2}*ε*from 0.15 to 0.05, the thermal loads

_{2}*ΔJ*(at

_{C}*T*= ~280

_{2}*K*) quickly decreases from ~0.6

*W/m*to ~0.2

^{2}*W/m*.

^{2}*T*also affects the thermal performance. As shown in Fig. 8 (left), higher

_{2}*T*puts more thermal load to the optical system space. In contrast, for the collimator space, higher

_{2}*T*makes

_{2}*ΔJ*closer to 0 in Fig. 8 (right). This becomes a balance problem between

_{H}*ΔJ*and

_{C}*ΔJ*. As an example, if the maximum allowable magnitude of the thermal load is 0.3

_{H}*W/m*for both

^{2}*ΔJ*and

_{C}*ΔJ*(for

_{H}*ε*=

_{1}*ε*= 0.9 and

_{3}*ε*= 0.1 case),

_{2}*T*may be chosen to be 252

_{2}*K*(green long dashed lines in Fig. 8).

*T*at 252

_{2}*K*, the effects of the other two plate’s temperatures

*T*and

_{1}*T*were investigated. While watching the thermal load change in the optical system space,

_{3}*T*was varied from 15

_{3}*K*to 45

*K*as shown in Fig. 9 (left). The thermal load

*ΔJ*was decreased as the 3rd plate got colder. The effect of

_{C}*T*on

_{1}*ΔJ*was small. The 1st plate’s temperature

_{C}*T*was changed from 299.9

_{1}*K*to 300.1

*K*to look at the effects on the collimator space

*ΔJ*. As shown in Fig. 9 (right), the magnitude of

_{H}*ΔJ*can be minimized (

_{H}*e.g.*0

*W/m*) by setting

^{2}*T*at an optimal temperature. The temperature of the 3rd plate

_{1}*T*hardly affects

_{3}*ΔJ*. (All three plots are overlapped in Fig. 9 (right).) In summary, once the emissivity values and

_{H}*T*are fixed,

_{2}*T*and

_{1}*T*may provide a good means to tweak the final thermal performance of a TS.

_{3}*T*at a certain temperature, the temperature of the 2nd plate was set to be float. In other words, the 2nd plate was not thermally controlled. The equilibrium temperature

_{2}*T*was determined based on the thermal emissive powers

_{2}*J*and

_{net_2 ±}*J*. The condition for the thermal equilibrium iswhere

_{net_3 ±}*ΔJ*is the thermal load on the second plate, and

_{2}*J*are the emissive powers depicted in Fig. 2.

_{net_2-3 ±}*T*was floating at its equilibrium temperature shown in Fig. 10 , and the thermal loads

_{2}*ΔJ*and

_{C}*ΔJ*were evaluated (Fig. 11 ). In comparison with the fixed

_{H}*T*case in Fig. 9, the thermal loads

_{2}*ΔJ*for the floating case showed slightly wider range of thermal loads in Fig. 11 (left). For

_{C}*T*= 320

_{1}*K*case,

*ΔJ*for the floating

_{C}*T*case in Fig. 11 (left) got slightly higher than the fixed

_{2}*T*= 252

_{2}*K*case in Fig. 9 (left), because

*T*at thermal equilibrium was ~269

_{2}*K*as shown in Fig. 10 (left). For

*T*= 280

_{1}*K*case,

*ΔJ*for the floating

_{C}*T*case in Fig. 11 (left) got slightly smaller than the fixed

_{2}*T*= 252

_{2}*K*case in Fig. 9 (left), because the equilibrium

*T*was ~236

_{2}*K*as shown in Fig. 10 (left). For

*ΔJ*, there was no significant difference between the floating and fixed

_{H}*T*cases because the floating temperature

_{2}*T*was changing in the very small range 252.2-252.4

_{2}*K*, which is practically same as the fixed

*T*= 252

_{2}*K*.

*T*approach is obvious. The 2nd plate does not need to be thermally controlled. The temperature

_{2}*T*is automatically fixed at the equilibrium temperature while the TS gives comparable thermal performance as the fixed

_{2}*T*case.

_{2}*K*optical system from a 300

*K*collimator. As shown in Fig. 9 and 11, the TS with holes occupying ~1% of the thermal plate area and with two black (

*i.e.*high emissivity) and a polished (

*i.e.*low emissivity) thermal plates accomplished thermal loads less than 200

*mW/m*for both the ambient and the cryogenic sides of the testing configuration. This is nearly 4 orders of magnitude attenuation from the 300

^{2}*K*collimator’s radiating power.

### 4.2 Optical performance of TS

*δx*and ±

*δy*. The hole diameter

*D*was also varied within ±

_{hole}*δD*. One of the simulation results is presented in Fig. 12 . The complex field at the last hole of a hole-set is distorted as a result of the misalignment and the hole diameter variation.

_{hole}*∆*and a phase error

_{a}*∆*were defined by integrating the complex field over the hole area as expressed in Eq. (20) and (21) to quantitatively assess the optical performance of the perturbed TS compared to the ideal one.

_{p}*Angle*is a function returns the phase angle of a complex field. These definitions simplify the representation and evaluation process of the test beam quality in ~85500 hole-sets.

*∆A value is present*since the intensity

*Q*is the square of amplitude

*A*. Variations in phase cause wavefront phase to change across the pupil, which degrade the performance of the collimator. The form of the wavefront phase or intensity variation follows the changes in hole size and position. For example, if all the holes are shifted by a same amount, the intensity will be decreased uniformly across the pupil. If holes in a small region are shifted relative to rest of the system, the intensity of the light in that region will be decreases and the wavefront phase in that region will be shifted.

*δx*,

*δy*, and

*δD*tolerance values in Fig. 13 .

_{hole}*δx*and

*δy*, causes more amplitude errors in the test beam as shown in Fig. 13 (left). For

*δx*=

*δy*=

*δD*= 100

_{hole}*μm*case, the RMS amplitude error is ~4.2%. If

*δx*and

*δy*are decreased to 50

*μm*, the RMS amplitude error is decreased by ~0.5%. If

*δD*is decreased to 70

_{hole}*μm*, the RMS amplitude error is decreased by ~1%. In other words, the amplitude error is more sensitive to the hole diameter tolerance, which has more direct impact on the energy blocked by the hole. This amplitude error may not be a big issue for most wavefront measurements, which are primarily dependent on the phase of the test beam.

*δx*,

*δy*and

*δD*are increased. While

_{hole}*δx*and

*δy*varies from 50

*μm*to 170

*μm*, the RMS phase error increases from ~0.001

*waves*to ~0.005

*waves*. The hole diameter tolerance

*δD*also affects the induced RMS phase error, but the impact is relatively small as shown in three different colors in Fig. 13 (right). The alignment tolerance is more important than the hole size tolerance to achieve higher quality test beam phase. The RMS phase error were <0.006

_{hole}*waves*RMS for all the tolerance ranges investigated in this section, which seems promising for most optical testing applications.

## 5. Concluding remarks

*K*system from a 300

*K*collimator. A three thermal plate TS will cause thermal loading less than 200

*mW/m*for both the ambient and the cryogenic sides of the system. The optical performance was demonstrated with the wave propagation simulation results showing that the wavefront degradation due to the TS was very small (

^{2}*e.g.*<0.006

*waves*RMS).

## Appendix

### A.1 Basic functions

*cyl(r),*which gives a circular disk in the

*x*-

*y*plane, is defined as below.

*somb(r)*, is defined using the first-order Bessel function of the first kind,

*J*.

_{1}## References and links

1. | M. Clampin, “Status of the James Webb Space Telescope (JWST),” Proc. SPIE |

2. | D. M. Chaney, J. B. Hadaway, J. Lewis, B. Gallagher, and B. Brown, “Cryogenic performance of the JWST primary mirror segment engineering development unit,” Proc. SPIE |

3. | S. C. West, S. H. Bailey, J. H. Burge, B. Cuerden, J. Hagen, H. M. Martin, and M. T. Tuell, “Wavefront control of the Large Optics Test and Integration Site (LOTIS) 6.5m collimator,” Appl. Opt. |

4. | D. W. Kim and J. H. Burge, “cryogenic thermal mask for space-cold optical testing for space optical systems,” in OF&T, OSA Technical Digest Series (Optical Society of America), FTuS2 (2010). |

5. | S. B. Hutchison, A. Cochrane, S. McCord, and R. Bell, “Update status and capabilities for the LOTIS 6.5 meter collimator,” Proc. SPIE |

6. | E. Hecht, |

7. | J. Goodman, |

**OCIS Codes**

(120.3940) Instrumentation, measurement, and metrology : Metrology

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: March 7, 2012

Revised Manuscript: May 10, 2012

Manuscript Accepted: May 11, 2012

Published: May 16, 2012

**Citation**

Dae Wook Kim, Wenrui Cai, and James H. Burge, "Use of thermal sieve to allow optical testing of cryogenic optical systems," Opt. Express **20**, 12378-12392 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-12378

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### References

- M. Clampin, “Status of the James Webb Space Telescope (JWST),” Proc. SPIE7010, 70100L, 70100L-7 (2008). [CrossRef]
- D. M. Chaney, J. B. Hadaway, J. Lewis, B. Gallagher, and B. Brown, “Cryogenic performance of the JWST primary mirror segment engineering development unit,” Proc. SPIE8150, 815008, 815008-12 (2011). [CrossRef]
- S. C. West, S. H. Bailey, J. H. Burge, B. Cuerden, J. Hagen, H. M. Martin, and M. T. Tuell, “Wavefront control of the Large Optics Test and Integration Site (LOTIS) 6.5m collimator,” Appl. Opt.49(18), 3522–3537 (2010). [CrossRef] [PubMed]
- D. W. Kim and J. H. Burge, “cryogenic thermal mask for space-cold optical testing for space optical systems,” in OF&T, OSA Technical Digest Series (Optical Society of America), FTuS2 (2010).
- S. B. Hutchison, A. Cochrane, S. McCord, and R. Bell, “Update status and capabilities for the LOTIS 6.5 meter collimator,” Proc. SPIE7106, 710618, 710618-12 (2008). [CrossRef]
- E. Hecht, Optics, 4th ed. (Pearson Education, 2002), Chap. 10.
- J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company Publishers, 2005), Chap. 4.

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