Passive Athermalization: Maintaining Uniform Temperature Fluctuations

Home , Athermalization, Catadioptric system

John Tejada, Janos Technology, Inc.

An optical system is athermalized if its critical performance parameters techniques can be customized for all types of optical systems. Optical (such as MTF, BFL, EFL, etc.,) do not change appreciably over the operating systems that can be athermalized temperature range. can consist of reflecting components (mirrors), refracting components or rotationally symmetric op- the limited battery or solar power (lenses), or a combination of both. O

tical systems, either the lens to energize motors it would take to Examples of how passive athermal- p

or the detector moves along maintain focus. Additionally, mo- ization is achieved for reflective and t

F i c

the optical axis to maintain opti- tors have limited lifetimes, add refractive optical systems will be a l

cal performance. If the compen- weight to launch payloads, and discussed using examples in the sating axial motion is accomplished cannot be easily serviced once de- subsequent sections. D e without the use of motors or other ployed in space. Therefore, it is s i active devices, then the optical sys- undesirable to use them unless Catoptrical systems g tem is considered passively ather- absolutely necessary. Catoptrical systems exclusively n malized. This article will discuss Hazardous environments can be use mirrors to form an image. Two the consequences of uniform tem- encountered when performing simple examples are the Cassegrain perature fluctuations solely, tasks such as nuclear power plant and the Gregorian mirror systems. thereby ignoring the impact of inspection and border patrol sur- The Cassegrain optical system is temperature gradients within the veillance where temperatures reach used here as an example. The optical system. extremes that are unsafe for con- equation that governs this 2-mirror The coefficient of thermal ex- stant human exposure. If the opti- system is given below. pansion (CTE) and the thermal co- cal system can be passively ather- efficient of refraction (TCR) are ma- malized, then the available power + – L = C ϕp ϕs ϕp ϕs ϕ terial properties of lenses and can be used for transmitting video housings that respond to temper- information or increasing opera- where ature changes within an optical tional time instead of activating = power of the primary mirror ϕp system. The following parameters motors to maintain focus. = power of the secondary mirror ϕs change as a result of uniform tem- To achieve passive athermalization, L = separation between the pri- perature variations: radii of cur- different temperature-compensating mary and secondary mirrors vature, refractive index of the lens material, refractive index of the lens medium (usually air), me- TABLE 1. chanical dimensions of lenses, and LENS PARAMETER VARIATIONS WITH TEMPERATURE the physical dimensions of the lens support structure. The parameter Parameter Variation Formulation variations with respect to temper- Radius of curvature R + ∆R R + dR/dT ature are detailed in Table 1. Refractive index of lens material n + ∆n n + dn /dT Passive athermalization is bene- L L L L ficial in optical systems that are Lens material thickness t + ∆t t + dn/dT isolated from direct human contact Refractive index of air nair +∆nair nair + dnair/dT or have limited access to power. Lens separations L + ∆L L + dL/dT Systems that are deployed in space, for example, cannot afford to use

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because the housing material ex- pands proportionally with the all-aluminum housing change of power in the mirrors. This aluminum is the simplest manner to passively primary athermalize an optical system for any temperature variation. If this example used different ma- aluminum terials for the primary, secondary secondary image and housing, the athermalization problem would become more com- plex; but the basic principles would remain the same. The primary power would change at a different rate than the secondary power, and the housing material would have f/2 all all-aluminum Cassegrain to be chosen such that the image EFL = 100 mm remained in focus. Reflecting sys- FFOV = 0.5° tems that are passively athermalized in this manner are more likely Figure 1. All-aluminum Cassegrain telescope. to experience other aberrations in addition to defocus when used at = total power of the Cassegrain applications, the discussion will be extreme temperatures. ϕC mirror system. limited to the other parameters. In some applications, the nominal A simple Cassegrain telescope In this example, the expansion off-axis performance of a catoptric n forms an image by using a primary coefficient of the primary and the system is insufficient, in which g i parabolic mirror which focuses en- secondary are identical to the hous- case, the catadioptric system may s

e ergy onto a secondary hyperbolic mir- ing material. Therefore the optical be employed. D

ror. A typical Cassegrain example is system remains in focus throughout l a Catadioptrical systems c

i Catadioptric lenses are hybrid op- t TABLE 2. tical systems that use both reflective p CATADIOPTRIC MATERIAL DATA

O and refractive elements in the optical design to achieve the desired per- Expansion Thermal Coefficient Material Coefficient of Refraction formance. These systems offer the advantage of improved off-axis opti- ␭ = 546.00 nm ␭ = 480.0 nm ␭ = 435.0 nm cal performance by reducing field Aluminum 236 E-7/°C — — — aberrations. For the sake of discus- NSF4 96.500 E-7/°C -0.10 E-6 1.27 E-6 2.63 E-6 sion, the Cassegrain design shown in section 1 will be modified by in- NPSK53 95.607 E-7/°C -3.80 E-6 -3.50 E-6 -3.19 E-6 serting a doublet near the image plane, and then re-optimizing the sur- faces for peak performance. The re- shown in Figure 1. The size of the the temperature range of –10 °C to sultant design is shown in Figure 3. obscuration is determined primarily +50 °C. For instance, as the tem- The power distribution of the op- by the aperture of the secondary. perature increases, the power of the tical elements in the catadioptric sys- The change in the effective focal primary and secondary mirrors gets tem is similar to a Cooke triplet with length (EFL) of the resultant mirror weaker. The image remains in focus the primary mirror as the positive system is scaled by the linear coefficient of thermal expansion. Yet the Cassegrain is still considered to be TABLE 3. passively athermal because the REFRACTING AFOCAL MATERIAL image plane remains in focus at vary- Expansion Thermal Coefficient ing temperatures. The ray fan plots Material Coefficient of Refraction in Figure 2 illustrate that the optical system remains focused. ␭ = 3000 nm ␭ = 4000 nm ␭ = 5000 nm The mirror parameters that Invar 5 E-7/°C — — — changed are the radii of curvature, Silicon 39.0 E-7/°C 160.3 E-6 169.3 E-6 177.9 E-6 separation of the mirrors, and the refractive index of the air. Assum- Germanium 61.0 E-7/°C 447.5 E-6 467.8 E-6 488.2 E-6 ing the index variation of air with temperature is small for these

H-342 THE 2006 PHOTONICS HANDBOOK Passive Athermalization

tangential sagittal tangential sagittal tangential sagittal 1.00 relative 1.00 relative 1.00 relative field height field height field height 1.0(0.250°) 1.0 1.0(0.250°) 1.0 1.0 (0.250°) 1.0

–1.0 –1.0 –1.0 –1.0 –1.0 –1.0

1.00 relative 1.00 relative 1.00 relative 1.0 field height 1.0 1.0 field height 1.0 1.0field height 1.0 (0.000°) (0.000°) (0.000°)

–1.0 –1.0 –1.0 –1.0 –1.0 –1.0

simple Cassegrain 600.000 nm simple Cassegrain 600.000 nm simple Cassegrain 600.000 nm optical path difference (waves) 550.000 nm optical path difference (waves) 550.000 nm optical path difference (waves) 550.000 nm 500.000 nm 500.000 nm 500.000 nm 29-Jul-05 29-Jul-05 29-Jul-05

Cassegrain ray fans Cassegrain ray fans Cassegrain ray fans at 20 °C at 50 °C at –10 °C O p t

Figure 2. Ray fans for simple Cassegrain. i c a l

element, the secondary mirror as As in the previous example, the of refraction (dn/dT) and the coef- the negative element, and the rear primary and secondary mirrors are ficient of thermal expansion for D e doublet as the positive corrector. made of the same material as the each element. s i The rear doublet consists of a neg- housing. However, the additional The change in the EFL of the g ative flint lens (NSF4) and a positive complication for the catadioptric resultant mirror system and dou- n crown (NPSK53) lens. The marginal system is the impact of the re- blet system is modified by both the ray height on the rear doublet is fracting doublet over temperature. CTE and TCR (dn/dT). Yet the small due to the proximity to the The TCR (dn/dT) and the CTE of Cassegrain is still considered to be image plane. Consequently the dou- each lens material pose an addi- passively athermalized because the blet has a lesser impact on focus tional complication to the passive image plane remains in focus at over temperature than the mirrors, athermalization issue. Table 2 higher and lower temperatures. The but cannot be ignored. shows the temperature coefficient ray fan plots in Figure 4 illustrate that the optical system remains focused. The plots are at room temperature and 50 °C. The plot all-aluminum housing at –10° C is nearly identical to the aluminum 50 °C plot. primary The coefficient of thermal ex- negative pansion impacts the radii of the lens (NSF4) doublet lenses in a similar fashion positive lens aluminum (NPSK53) that was illustrated by the catoptric secondary example (i.e., the radii become weaker as the temperature in- doublet creases). However, the CTE of each image doublet material is less than half of the aluminum expansion coefficient used for the housing. Therefore, the TCR of each lens must be f/2 catadioptric system carefully chosen in order to com- EFL = 100 mm pensate for the different thermal FFOV = 0.5 ° expansion coefficients if the optical system is to remain in focus. Figure 3. Catadoptric optical system. In this example, the TCR for the negative lens is positive, causing

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1.00 relative 1.00 relative 1.00 relative tangential sagittal tangential sagittal tangential sagittal field height field height field height (0.250°) (0.250°) (0.250°) 1.0 1.0 1.0 1.0 1.0 1.0

–1.0 –1.0 –1.0 –1.0 –1.0 –1.0

1.00 relative 1.00 relative 1.00 relative field height field height field height 1.0 (0.000°) 1.0 1.0 (0.000°) 1.0 1.0(0.000°) 1.0

–1.0 –1.0 –1.0 –1.0 –1.0 –1.0

simple catadioptric 546.000 nm simple catadioptric 546.000 nm simple catadioptric 546.000 nm optical path difference (waves) 480.000 nm optical path difference (waves) 480.000 nm optical path difference (waves) 480.000 nm 435.000 nm 435.000 nm 435.000 nm 08-Aug-05 08-Aug-05 08-Sept.-05

Cassegrain ray fans Cassegrain ray fans Cassegrain ray fans at 20 °C at 50 °C at –10 °C n g i Figure 4. Ray fans for a catadioptric system. s e D

the lens to grow more temperature range. In some more l

a negative as the tempera- demanding applications, a further c positive negative i ture increases. Likewise, constraint restricting the magnifica- t the positive lens has a silicon germanium tion change over the temperature p objective eyepiece

O negative TCR, which range may be specified. makes the lens less pos- The magnification of these systems itive as the temperature is given by increases. The overall ef- ϕL2 M= fect is to cause the power ϕL1 of the rear doublet to become weaker as the tem- Figure 5 is an example of a perature increases and Invar housing Galilean telescope operating from thereby compensate for 3.0 to 5.0 µm. the effects of the expand- mid-wave Galilean telescope The change in collimation of the ing aluminum housing. MAG = 2.35 exiting beam of the refracting afo- FFOV) = 0.5 ° cal system is modified by both the Refractive afocals CTE and TCR for the optical mate- The Galilean telescope rials and the housing. The thermal is an afocal arrangement Figure 5. Galilean refracting telescope. coefficients for these materials are of positive and negative shown in Table 3. lenses which can be used to expand = power of lens 1 (the front For this example, the paraxial ϕL1 beams or change fields-of-view. The element) change in collimation is about 18 last example for examination is a = power of lens 2 (the back µrad (well within the diffraction ϕL2 Galilean telescope consisting of two element) limit). The change in collimation as lenses used in the mid-wave in- D = distance between the traced by the ray fans is within the 1 frared portion of the spectrum. The principle planes of the ⁄4 wave Raleigh criteria as shown equation that describes this opti- elements below. As in the Catadioptric ex- cal system is given below. Note that ϕAFO = power of the afocal ample, the ray fans at –10 °C and this equation is very similar to system, which by 50 °C are shown in Figure 6. Equation 1. definition is zero. The housing material selected for Optical systems of this type are this example is INVAR (a nickel- + - D = = 0 considered passively athermalized iron alloy). This material has a very ϕL1 ϕL2 ϕL1 ϕL2 ϕAFO if energy exiting the last lens re- low expansion coefficient compared where mains collimated over the operating with aluminum or other metals.

H-344 THE 2006 PHOTONICS HANDBOOK Passive Athermalization

1.00 relative 1.00 relative 1.00 relative tangential sagittal tangential sagittal tangential sagittal field height field height field height (0.250°) (0.250°) (0.250°) 0.25 0.25 0.25 0.25 0.25 0.25

–0.25 –0.25 –0.25 –0.25 –0.25 –0.25

1.00 relative 1.00 relative 1.00 relative field height field height field height 0.25 (0.000°) 0.25 0.25 (0.000°) 0.25 0.25 (0.000°) 0.25

–0.25 –0.25 –0.25 –0.25 –0.25 –0.25

galilean telescope 5000 nm galilean telescope 5000 nm galilean telescope 5000 nm optical path difference (waves) 4000 nm optical path difference (waves) 4000 nm optical path difference (waves) 4000 nm 3000 nm 3000 nm 3000 nm 30-Aug-05 30-Aug-05 30-Sept.-05

Cassegrain ray fans Cassegrain ray fans Cassegrain ray fans at 20 °C at 50 °C at –10 °C O Beam expander ray fans. Figure 6. p t i c

The positive objective lens is spher- that the eyepiece lens becomes more can be achieved in reflective sys- a l

ical and is made of silicon. It has a negative as the temperature in- tems, hybrid systems and refrac- small coefficient of expansion and a creases. Therefore, when these tive systems. Additionally, passive D e moderately large positive thermal lenses are used in an afocal config- athermalization can be achieved by s i coefficient of refraction. This indi- uration and mounted in INVAR, their choosing the housing material g cates that the lens would get more dimensional and material changes to be identical to the optical mate- n positive as the temperature in- offset each other such that the rial, choosing the optical compo- creases. Similarly, the negative ger- exiting beam remains collimated. nent properties to compensate for manium lens of the eyepiece also Additionally, the change in magnifi- the housing material, and choos- has a small expansion coefficient cation is only about 0.3 percent. ing the housing material to com- and a large positive thermal coeffi- The examples in this article pensate for the optical properties cient of refraction. This indicates illustrate that passive athermalization of the components. ᮀ