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Optical design of high resolution concave superposition compound eye

Ayatollah Karimzadeh

Open Access Open Access

Abstract

A compound eye is a way to reach miniature imaging systems. This paper discusses design and image evaluation of novel high resolution concave superposition compound eyes with a planar or curved detector. In the superposition system, each channel images all of fields of view of the system. This designed system contains three curved micro lens arrays with aspheric surfaces for the concave superposition eye. We have simulated and optimized a high resolution system by using geometrical and diffraction-based methods.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The interest in miniaturizing imaging systems has been recently increased. Compound eye is a way to reach small size imaging systems. Compared to conventional imaging systems, natural Compound eye has the advantage of compact structure, high sensitivity to motion and large field of view (FOV).

With recent improvements of image sensors and microlens arrays technology the interest in miniaturizing imaging systems such as compound eye systems has been increased [1–3].

There are two different types of compound eyes, the apposition and the superposition compound eyes [1–4].

In the apposition eye system each channel only transfers a portion of the overall field of view (FOV) and the adjacent channel’s FOVs are attached to each other. On the other hand, in the superposition compound eye each channel can transfer the full FOV of the system.

Previous work on superposition compound eyes design concentrated on planar microlens arrays [1–8].

In this paper, design and optimization of the concave superposition compound eye with both curved and planar detector is presented. The designed system consists of three microlens arrays. Aspherical surfaces are introduced to improve the image quality.

The text is organized as follows. In section 2 the concave superposition compound eye is discussed and paraxial ray tracing of microlens array for superposition compound eye simulation is reported. In section 3 the design and optimization of a concave superposition eye reported. Conclusions are drawn in Section 4.

2. Basics of concave superposition compound eye

In a natural superposition Compound eye, each channel consists of a grin lens with a negative angular magnification so that the rays from each point of the object in different channels finally reach the same imaging point [7,8].

The designed superposition compound eye is an array of the same optical channels that consist of three microlens. Each one of these channels images a section of a total field of view (FOV) in a single point. The partial images formed by the multiple channels will superimpose at the image plane [4, 5,7].

The geometrical optics concepts for the concave spherical superposition compound eyes are shown in Fig. 1.

 figure: Fig. 1.

Fig. 1. Layout of superposition compound eye consisting of microlens arrays.

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Each channel of the concave superposition compound eyes need to have positive EFL (effective focal length) for magnification of chief ray angle (Fig. 2).

 figure: Fig. 2.

Fig. 2. One channel layout

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As shown in Fig. 1 multiple channels are aligned on a concave sphere with a certain radius and all optical axes intersect at its center. In this case, images from several channels are superimposed on a planar or concave detector.

System design begins with the paraxial modeling of the system and calculating principle ray magnification in one channel.

As shown in Figs. 1 and 2, the object axial rays in different channels must reach the same imaging point, for this case we have (assuming θ1 and θ2 are small):

$$\frac{{{\boldsymbol{\theta}}_2} - {{\boldsymbol{\theta}}_1}}{{\boldsymbol{\theta}}_1} = \frac{\textrm{R}}{{\textrm{BFL}}}$$
Equation (1) shows the relation between principle ray magnification in each channel with its BFL (back focal length) and arrays sphere radius.

The ray trace matrix A, in each channel (Figs. 1 and 2) after passing through the three microlenses is (t3 = BFL):

$$A = \left[ {\begin{array}{{cc}} 1&{ - \frac{1}{{{f_3}}}}\\ {{t_3}}&{1 - \frac{{{t_3}}}{{{f_3}}}} \end{array}} \right]\left[ {\begin{array}{{cc}} 1&{ - \frac{1}{{{f_2}}}}\\ {{t_2}}&{1 - \frac{{{t_2}}}{{{f_2}}}} \end{array}} \right]\left[ {\begin{array}{{cc}} 1&{ - \frac{1}{{{f_1}}}}\\ {{t_1}}&{1 - \frac{{{t_1}}}{{{f_1}}}} \end{array}} \right]$$
The output ray height y’ and angle θ’ are calculated from the known input ray height y and the paraxial input ray angle θ using the following equation [5]:
$$\left[ {\begin{array}{{c}} {\theta^{\prime}}\\ {y^{\prime}} \end{array}} \right] = A\left[ {\begin{array}{{c}} \theta \\ y \end{array}} \right]$$
For the principle ray which passes from the center of the first microlens (yp = 0) the output ray is:
$${\theta _2} = {A_{11}}{\theta _1} + {A_{12}}{y_p} \to $$
$${\theta _2} = \left[ {1 - \frac{{{t_1}}}{{{f_2}}} - \frac{1}{{{f_3}}}\left( {{t_1} + {t_2} - \frac{{{t_1}{t_2}}}{{{f_2}}}} \right)} \right]{\theta _1}$$
$$\frac{{{\theta _2} - {\theta _1}}}{{{\theta _1}}} ={-} \frac{{{t_1}}}{{{f_2}}} - \frac{{{t_1}}}{{{f_3}}} - \frac{{{t_2}}}{{{f_3}}} + \frac{{{t_1}{t_2}}}{{{f_2}{f_3}}} = \frac{R}{{{t_3}}}$$
By using Eq. 5 we choose initial parameters of the spherical superposition compound eye.

The aperture of the field lens also plays the role of field diaphragm to limit the FOV of the channel.

3. Design of concave superposition compound eye

From Eqs. (3) and (5) we choose the geometry of the system (consists of array curvature, distance between arrays, EFL of microlenses and …) and the starting point of the design. we design a 5×1 array system with a total length of 3.3 mm, BFL of 1.9mm, 8° FOV (one channel maximum FOV is 15°) and image size of 1.4 mm. We choose the first array curvature radius −6.02mm. The focal length of each channel is + 9mm.

We optimize the system to reach a high resolution concave superposition compound eye. We choose high MTF values as optimization target. MTF of ideal superposition compound eye is calculated by HR Fallah, A. Karimzadeh [5]. In MTF calculation we (same as OSLO optical design software) assumed that the images are coherent with respect to each other.

As shown in Fig. 3 the designed channel is composed of three microlenses with specifications given in Table 1. The principle ray magnification is 4× (input and output angles are 7.5° and 30° respectively).

 figure: Fig. 3.

Fig. 3. One channel layout of superposition compound eye

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Tables Icon

Table 1. One channel surfaces specifications

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The aberrations are computed with respect to the paraxial image. Optimizing the aberrations and increasing the channel’s MTF guarantee decreasing superposition eye aberrations and improvement of its resolution.

Raytracing results demonstrate that the all rays from the one FOV are focused at the same imaging point on the detector (Fig. 4).

 figure: Fig. 4.

Fig. 4. Layout of concave superposition compound eye

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To assess the image quality, the aberration and modulation transfer function (MTF) of a channel for different linear fields of view considering different wavelengths in the visible range are calculated. The results are shown in Fig. 5.

 figure: Fig. 5.

Fig. 5. MTF of one channel of superposition compound eye.

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To evaluate the image quality, MTF for different wavelengths is studied at total FOV. In OSLO it assumed that the images are coherent with respect to each other. The curved image surface is replaced by a flat surface (flat detector). By replacing the curved image surface by a flat surface (flat detector) we see that MTF do not show significant changes. The MTFs of superposition compound eye (all channels) at 60 cycles/mm are about 0.2 (Figs. 5 & 6).

 figure: Fig. 6.

Fig. 6. MTF of superposition compound eye (all channels).

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The designed superposition compound eye (all channels) spot diagrams are shown in Fig. 7. The spot size is smaller than 0.04 mm.

 figure: Fig. 7.

Fig. 7. Spot diagram of superposition compound eye (all channels).

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We can design systems with larger number of microlens in each array by the same way.

4. Conclusions

High resolution concave superposition compound eye has been achieved. In this paper we design a concave superposition compound eye in which each channel images all of the FOV of the system. This design can aid in better understanding the work of concave superposition compound eye systems.

Acknowledgements

The author is grateful to the Amirkabir University of Technology (AUT) research office for their support.

References

1. R. Völkel, M. Eisner, and K. J. Weible, “Miniaturized imaging systems,” Microelectron. Eng. 67-68, 461–472 (2003). [CrossRef]  

2. T. Nakamura, R. Horisaki, and J. Tanida, “Computational superposition compound eye imaging for extended depth-offield and field-of-view,” Opt. Express 20(25), 27482–27495 (2012). [CrossRef]  

3. J. Duparré, P. Schreiber, A. Matthes, E. Pshenay-Severin, A. Bräuer, A. Tünnermann, R. Völkel, M. Eisner, and T. Scharf, “Microoptical telescope compound eye,” Opt. Express 13(3), 889–903 (2005). [CrossRef]  

4. A. Garza-Rivera and F.-J. Renero-Carrillo, “Design of Artificial Apposition Compound Eye with Cylindrical Micro-Doublets,” Opt. Rev. 18(1), 184–186 (2011). [CrossRef]  

5. H. R. Fallah and A. Karimzadeh, “MTF of compound eye,” Opt. Express 18(12), 12304–12310 (2010). [CrossRef]  

6. J. Duparré, P. Schreiber, and R. Völkel, “Theoretical analysis of an artificial superposition compound eye for application in ultra at digital image acquisition devices,” in Optical systems design, Proc. SPIE 5249, SPIE, (St. Etienne, France), September 2003.

7. HR Fallah and A. Karimzadeh, “Design and simulation of a high-resolution superposition compound eye,” J. Mod. Opt. 54(1), 67–76 (2007). [CrossRef]  

8. N. Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A: Pure Appl. Opt. 4(4), S1–S9 (2002). [CrossRef]  

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Figures (7)
Fig. 1.
Fig. 1. Layout of superposition compound eye consisting of microlens arrays.

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Fig. 2.
Fig. 2. One channel layout

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Fig. 3.
Fig. 3. One channel layout of superposition compound eye

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Fig. 4.
Fig. 4. Layout of concave superposition compound eye

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Fig. 5.
Fig. 5. MTF of one channel of superposition compound eye.

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Fig. 6.
Fig. 6. MTF of superposition compound eye (all channels).

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Fig. 7.
Fig. 7. Spot diagram of superposition compound eye (all channels).

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Tables (1)

Tables Icon

Table 1. One channel surfaces specifications

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Equations (6)

Equations on this page are rendered with MathJax. Learn more.

θ 2 − θ 1 θ 1 = R BFL
A = [ 1 − 1 f 3 t 3 1 − t 3 f 3 ] [ 1 − 1 f 2 t 2 1 − t 2 f 2 ] [ 1 − 1 f 1 t 1 1 − t 1 f 1 ]
[ θ ′ y ′ ] = A [ θ y ]
θ 2 = A 11 θ 1 + A 12 y p →
θ 2 = [ 1 − t 1 f 2 − 1 f 3 ( t 1 + t 2 − t 1 t 2 f 2 ) ] θ 1
θ 2 − θ 1 θ 1 = − t 1 f 2 − t 1 f 3 − t 2 f 3 + t 1 t 2 f 2 f 3 = R t 3
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