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Several state-of-the-art imaging applications require a large operational spectral band, a large field size, and a high numerical aperture (NA). The design of a lens that simultaneously meets these requirements is a challenging task. We present optical designs of hyper NA imaging systems that comprise a multi reflection optical element. Light entering this element reflects multiple times before exiting. The present lens designs are 1.65 NA imaging system that operate in the broad spectral band [486.1 ~656.3 nm], have field size of 1.75 mm, and 20X magnification.
©2013 Optical Society of America
1. Introduction
High Numerical Aperture (NA) imaging systems are used in several areas such as optical lithography, inspection, and microscopy. Several imaging applications require as well large operational spectral band and field size. For some imaging systems small obscuration is also required. Some state of the art lens designs can achieve large NA and field size but at a narrow operational spectral band [1, 2]. Other lens designs operate at large spectral band but have very small field size [3, 4]. The design of a lens that simultaneously meets all these requirements is a challenging task. In this paper we present a Multi Reflection Element (MRE) that causes light to reflect multiple times before it travels to the next the element. Two surfaces – four reflections optical systems have been previously reported using mirrors in air [5, 6].
This paper is organized as follows. In section 2 we discuss the various design configurations for high NA imaging systems. The design configuration used for two designs presented in this paper is also discussed. In section 3 we present three different 1.65 NA lens designs. The first lens design doesn’t use MRE. The second and third lens designs use MRE. And we conclude our presentation in section 4.
2. High NA lens design configurations
Four main design configurations have been used for high NA imaging systems; Total Internal Reflection (TIR), Dioptric, Catoptric, and Catadioptric [7–10]. The TIR design configuration suffers from relatively large central obscuration. The dioptric, or all refractive, design configuration is the standard for visible microscopy. As NA increases, the correction of chromatic aberrations becomes challenging. In addition, the total length is relatively large. The Catoptric design configuration, or all reflective has relatively large central obscuration. In addition, available degrees of freedom, needed for aberrations compensation, are relatively small compared to the dioptric design configuration. The Catadioptric design configuration is a compromise between the all refractive and the all reflective design configurations. Available degrees of freedom allow better aberrations control. On the other hand the chromatic aberrations induced by lenses are appreciable and contribute significantly to the final image quality. In this paper, we explore and use the Catadioptric design configuration.
The first element is a glass shell that reduces the angle of the incident rays. As shown in Fig. 1, a ray incident onto the shell, travelling at large angle, undergoes two reflections and exits the shell at a smaller angle. The aberrations induced by the shell are balanced by a following group of optical elements. The complexity of the following optical elements, system obscuration and total length are defined by the glass shell.
Given the paraxial magnification (Mo), the obscuration (ko), and the total length (Lo), the shell reflecting surfaces radii of curvatures can be formulated as a function of the axial distances (t1 and t2).
whereØ1 is the power of right surface or primary mirror, and the obscuration is defined as follows.where θm and θap are the angles of the marginal ray and the ray hitting primary mirror at the aperture edge. Notice that Eqs. (1) – (4) are based on paraxial assumption and can only be used to get an initial estimate of R1 and R2. To calculate the accurate values, the error in obscuration value is used to modify ko and new R1 and R2 are recalculated. After few iterations actual obscuration matches preset value and precise values of R1 and R2 are obtained. A combination of optical elements is then designed to balance aberrations induced by the glass shell. Various configurations of t1 and t2 can be tried out to find out the best combination.A commonly used configuration of the solid shell comprises a flat secondary mirror. Light is focused near the primary mirror vertex [2]. To analyze the value of this configuration a solid shell with a flat secondary and an aspheric primary concave mirrors are optimized at different values of central thickness. The angle of the marginal ray reflecting off the secondary mirror is shown in Fig. 2(a) to be larger than the critical angle. This is in the case of an image plane at the vertex of the primary mirror. TIR can be avoided when the image plane is shifted to the right of the primary mirror vertex. In Fig. 2(b) the central thickness is set constant at the value used in design 1 that will be shown latter. The image plane is shifted to the right of the vertex of the primary mirror and the angle of marginal ray reflecting off the flat secondary mirror is plotted. For each case the shell is optimized for best image quality. At 20 mm of image plane shift, marginal ray angle is slightly smaller than the critical angle and obscuration is 0.37. The color correction over the visible range is not an easy task for such large angles at the glass air interface. In addition, the magnification of this design configuration is small. To illustrate the secondary mirror power is changed from 0 to −0.133 and the primary mirror is optimized. As shown in Fig. 3(a), the shell paraxial magnification is about −2 for a flat secondary mirror. For large magnification the secondary mirror has to be convex. The target overall magnification is −20. To relax the design of the following group of optical elements, solid shell has to provide large magnification. On the other hand a convex secondary mirror will induce appreciable change in shell overall Petzval curvature as shown in Fig. 3(b).
Fig. 2 Marginal ray angle, after reflection off flat mirror is greater than the critical angle when (a) image plane is set at the primary mirror vertex and slightly smaller than the critical angle when (b) image plane is shifted.
Fig. 3 (a) Solid shell paraxial magnification versus secondary mirror power. (b) Petzval curvature variation with secondary mirror power.
3. Hyper NA imaging system lens designs using MRE
In this section we present designs of 1.65 NA immersion imaging systems that operate in the broad spectral band [486.1 ~656.3 nm], have a field size of 1.75 mm, 0.25 mm object Working Distance (WD), and 20X magnification. The refractive index of the immersion medium is 1.77 at 0.58 µm. This corresponds to an angle of incident inside the immersion medium of ± 68°.
The first design configuration is shown in Fig. 4(a). A solid glass shell is used to reduce the angle of the incident rays. Glass shell induced aberrations are balanced by those of a following group of lenses. The glass shell has to have large magnification (1) to reduce the following group of lenses design complexity and (2) to allow light to exit at small angle for a relaxed color correction of the entire system. As discussed in section 2, a large magnification requires a convex secondary mirror. The drawbacks are (I) a strong Petzval surface with un favored sign and (II) a small working distance which increases the obscuration. To illustrate a solid glass shell is optimized under constrained obscuration and working distance. Magnification is the same for all cases. The optimized system Petzval radius of curvature is plotted in Fig. 5 versus combinations of obscuration (black) and working distance (red). As shown in Fig. 5, reducing obscuration makes Petzval surface stronger unless working distance is set loose. The use of convex secondary mirror limits obscuration. The final design is shown in Fig. 4(a). Design 1 has a diffraction limited image quality and a 60% obscuration.
Fig. 4 Hyper NA imaging system designs. (a) Design 1 doesn’t use MRE. Designs (b) 2 and (c) 3 uses MRE.
MRE is a glass shell with two reflecting surfaces designed such that light reflects multiple times before exiting it. In Fig. 6 we show 2, 4, and 6 MREs. MRE is designed to balance Petzval curvature induced by the glass shell. Integrating 6 reflections MRE with design 1 releases the constraint on the working distance. The solid shell is no longer the first element. Consequently the obscuration of the solid shell can be lowered to the desired value. The final design, shown in Fig. 4(b) has an obscuration of 30%, a total length that is 15% smaller than design 1, and a diffraction limited image quality.
MRE number of reflections and central thickness control MRE obscuration and Petzval curvature. To illustrate 2, 4, and 6 reflections MREs, shown in Fig. 6, are optimized with angle of incidence set to 68° and angle of exit constrained to 58°. The central thickness is changed from 10 to 17.5 mm and MRE is optimized for the best image quality and the smallest obscuration. MRE obscuration and Petzval radius of curvature are plotted versus central thickness in Figs. 7(a) and 7(b). It’s clear that the larger the number of reflections the smaller the obscuration and the weaker the Petzval surface. Figure 7(b) shows the larger the number of reflections the smaller the central thickness for a given amount of Petzval curvature. 6 reflections MRE is chosen to combine with design 1 since it provides the necessary Petzval correction at minimum central thickness. Combinations of 4 or 2 reflections MRE with design 1 might be other solutions that we may explore in future work.
Fig. 7 2, 4, and 6 reflections MRE (a) obscuration and (b) Petzval radius of curvature versus central thickness.
Design 3, shown in Fig. 4(c), comprises a four reflections MRE integrated to another design configuration. Two Mangin mirrors are used. These two mirrors form an intermediate image of the object. Following group of lenses reimages the intermediate image onto the final image plane. Having the two intermediate images close to apertures of the mirrors enables obscuration to be smaller. The use of MRE enables operation at NA as large as 1.65. In the absence of MRE light is subjected to total internal reflection at the edge of first mangin mirror. The use of 2 reflections MRE might be another solution that we may consider in future work. The image quality of design 3 is diffraction limited.
Specifications of the presented three designs are compared in Table 1. Designs 2 and 3 are 15% and 25% shorter than design 1. Design 3 is 17% smaller in diameter compared to design 1. Obscuration of designs 2 and 3 is half that of design 1. The polychromatic Root Mean Square (RMS) wave front error for the three designs is plotted in Fig. 8 versus field.
Table 1. Designs 1, 2, and 3 specifications.
4. Conclusion
We show that imaging systems with hyper immersion NA, large field size, large spectral band, small size, and small obscuration can be designed. We present lens designs of 1.65 NA imaging system that operate in the broad spectral band [486.1 ~656.3 nm], have field size of 1.75 mm, and 20X magnification. Designs 2 and 3 have 30% obscuration. We propose the use of an optical element that causes light to reflect multiple times before exiting. Designs 2 and 3 use MRE as the first element. All presented designs have diffraction limited image quality.
References and links
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