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Graphically Selecting Optical Material for Color Correction and Passive Athermalization

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Graphically Selecting Optical Material for Color Correction and Passive Athermalization Raghad Ismail Ibrahim.Int. Journal of Engineering Research and Applications ww.ijera.com ISSN: 2248-9622, Vol. 6, Issue 4, (Part - 5) April 2016, pp.38-41 RESEARCH ARTICLE OPEN ACCESS Graphically Selecting Optical Material for Color Correction and Passive Athermalization Raghad Ismail Ibrahim * *(Physics Department, Al-Mustansiryah University, and CollegeOf Education) ABSTRACT This paper presents pair optical glass by using a graphical method for selecting achromatize and athermalize an imaging lens. An athermal glass map that plots thermal glass constant versus inverse Abbe number is derived through analysis of optical glasses in visible light. By introducing the equivalent Abbe number and equivalent thermal glass constant, although it is a multi-lens system, we have a simple way to visually identify possible optical materials. ZEMAX will be used to determine the change in focus through the expected temperature changes in Earth orbit. The thermal defocuses over -20°C to +60°C are reduced to be much less than the depth of focus of the system. Keywords-Athermal glass, ZEMAX, graphical method for selecting, athermalize lens. I. INTRODUCTION Order to solve these difficulties, in this Athermalization is the principle of paper we introduce the equivalent Abbe number and stabilizing the optical performance with respect to equivalent thermal glass constant. Even though a temperature. Any temperature changes experienced lens system is composed of many elements, we can by the optics may be with respect to time or space or simply identify a pair of materials that satisfies the both. Time refers to a uniform heat soak across all athermal and achromatic conditions, by selecting the the optics, and space refers to a gradient across the corresponding materials for an equivalent lens from optics resulting in each lens (and housing) being a an athermal glass map and test them by application different temperature, or there being a radial change of Zemax software for a good solution. in temperature across an optic. Athermal systems are highly desirable for a multitude of applications in the II.THERMAL DEFOCUS broad field of integrated optics such as mobile phone The variations of temperature change the and black box cameras, so, it is important to develop radius of curvature, lens thickness and air spacing, an athermal optical system: an optical system that is and refractive index. These changes cause alignment insensitive to an environment’s thermal change and errors and degrade the optical performance.An the resulting system defocus. To reduce thermal and athermal system is meant to have stable optical chromatic errors, many design methods have been performance, even during temperature changes in reported. Perry studied the effect of temperature the optical system [6]. changes on optical performance in infrared optics. Table 1 lists the quantitative variations of Rogers showed that the multi-lens system could be design parameters due to temperature change [7], the achromatized and athermalized with three materials parameters of n (T), R (T), t (T), and L (T) are by solving three equations, but it was difficult to find measured values after temperature change. The a proper combination of materials [1].As alternative coefficients of a linear thermal expansion (CTE) are approaches to overcome these problems, graphic designated as αg for the lens material and αm for the methods have been developed. Rayces and Lebich housing material, respectively. proposed a γV-V diagram and showed that chromatic aberration corresponds to the area of a Table 1. Variations of design parameters due to triangle [2]. Tamagawa, et al. suggested other Temperature change [8]. graphical approaches by plotting the thermal dispersive power versus chromatic dispersive power and included a discussion of selecting the element powers in addition to the element materials [3, 4]. Schwertz studied how developing an optical system that is insensitive to an environment’s thermal change and the resulting system defocus [5], this research has been performed mainly on infrared optics, and there are few studies on visible optics. In www.ijera.com 38|P a g e Raghad Ismail Ibrahim.Int. Journal of Engineering Research and Applications ww.ijera.com ISSN: 2248-9622, Vol. 6, Issue 4, (Part - 5) April 2016, pp.38-41 The parameter dn/dT denotes the variation 휙 1 = 푇1 (7) of the refractive index with temperature. 휙 푇1 − 푇2 The expansion and contraction of a material due to 휙2 푇2 temperature changes is governed by a material’s = − (8) 휙 푇1 − 푇2 coefficient of thermal expansion, α, which has units If we design a doublet where the of 10-6m/°C (or ppm/°C). The change in length (L) achromatic doublet and athermal doublet equations of a material due to a temperature change is given by are all satisfied (Equations 5-8), the result is an Equation 1. achrothermic system: a system that is both 훥퐿 = 훼퐿훥푇 (1) achromatic and athermal as shown in Equation 9: Thermal defocus is the change in the focus 1 2 position on axis with temperature changes due to the = (9) 푇1 푇2 variation of the index of refraction with temperature IV. GRAPHICAL METHOD FOR (dn/dT) and the expansion of the material. The CHOOSING ACHROTHERM analogous equation quantifying the change in focal GLASS : length of a lens in air with temperature is given by By plotting the therm-optic coefficient (γ) Equation2: vs. the inverse color ν-number [9], we can visually 훥푓 = 훾푓훥푇 (2) identify two materials that can be used to develop an Where γ is the therm-optic coefficient. achrothermic system, this method not only helps γ can be defined using Equation 3: 1 푑푛 identify two available optical materials, but also 훾 = − 훼 (3) helps identify the CTE of the housing material 푛 − 1 푑푇 required for a housed achrothermic solution. As Whereα is Coefficient of linear thermal expansion 1 푑푟 1 푑푟 shown in Figure 1, the y-intercept provides the 훼 = 1 = 2 required housing material via a line that extends 푟1 푑푇 푟2 푑푇 through two materials and crosses the y-axis. In the case that a single housing material with the required III. ACHROMATIC & ATHERMAL CTE is unavailable, the required CTE can be DOUBLET EQUATIONS achieved using a bimetallic housing or alternative A common optical element is the mechanical mounting solution. achromatic doublet, which uses a positive and Figure 1 shows the athermal glass map for negative element of different materials with equal Schott glass [10]. Involves plotting the thermal glass and opposite amounts of chromatic aberration to constant versus the inverse Abbe number, we can correct for color. Assuming an element is in air, the visually identify two materials that satisfy the ν-number (inverse dispersion) for an arbitrary athermal and achromatic conditions [11] . waveband defined by the longest, shortest, and middle wavelength is given by Equation 4: 푛 − 1 = 푚푖푑 (4) 푛푠푕표푟푡 − 푛푙표푛푔 If Equations 5 and 6 are satisfied, the result is an achromatic doublet, each element is required to have power: 휙 푣 1 = 1 (5) 휙 1 − 2 휙 2 = − 2 (6) 휙 1 − 2 The optimal solution is one that has two elements with the largest ν-number difference: Δν. Fig. 1. Athermal glass map plotting γ v.s. 1/for A larger Δν results in longer focal lengths visible Schott glasses. (lower power) and shallower radii (reduces aberrations and increases optical performance). By In Fig. 1, any two materials (M1, M2) that looking at the glass map, it is simple to visually can be connected by a line that passes through the select a crown and flint glass that have a large ν- origin will provide athermal and achromatic number difference. Analogously, we can use the solutions. In other words, if one material is known inverse of the therm-optic coefficient (equation), on an athermal glass map, like M1(1/v1, γ1), then usually called the thermal ν number, in our another material(M2) that serves color correction achromatic equations to design an athermal double and passive athermalization can be found on a line as follows in Equations 7 and 8: connecting two materials. Even if a lens system is composed of many elements, the equivalent Abbe www.ijera.com 39|P a g e Raghad Ismail Ibrahim.Int. Journal of Engineering Research and Applications ww.ijera.com ISSN: 2248-9622, Vol. 6, Issue 4, (Part - 5) April 2016, pp.38-41 number and equivalent thermal glass constant reduce Thickness should be changed in the design the problem to be that of a two-element system as a above when a pair of glasses tested every time until doublet. Unlike some of the previous methods using the image shows clear. The lens layout for double complex triangle geometry [3, 4]. design in Fig.3. V. RESULT AND DISCUSSION We will use the method as shown in Fig.1 to visually determine exactly what material is required to achromatize and athermalize the multi- lens system. We know we want the slope of two different materials to be equal in order to achieve color correction and athermalization; any two materials that can be connected by a line that passes Fig.3. Optical Layout for athermal double design. through the origin will provide an achrothermic solution as shown in table 2. The important thing in athermal design is Table 2. Achrothermic Glasses Used in a Double the RMS spot diagram, which shows that with design. refocusing, the optical performance holds up well Number of Glass 1 Glass 2 over the field of view for extreme observing double temperature. Blur sizes at ‐100⁰C, 0⁰C, and +100⁰C achromatic lens (from left to right) shown in Fig .4. 1 N-FK5 F2 2 N-PSK53 SF66 3 BK10 N-BASF2 4 N-KZFS11 N-SF66 Table 2 would provide athermal glasses solution in air for visible.
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