Passive Athermalization: Maintaining Uniform Temperature Fluctuations 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 WWW.PHOTONICSDIRECTORY.COM H-341 Passive Athermalization 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 athermal- ized 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 opti- cal 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 coef- ficient 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 opti- cal 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.