Optics optimization in high-resolution imaging module with extended depth of field

Optics Optimization in High-Resolution Imaging Module with

Extended Depth of Field

Xi Chen*a, Dmitry Bakin

a, Changmeng Liu

a, Nicholas George

b

aAptina Imaging, 3080 North 1

st Street, San Jose, CA, USA 95134-5134

bThe Institute of Optics, University of Rochester, Rochester, New York, USA 14627

ABSTRACT

The standard imaging lens for a high resolution sensor was modified to achieve the extended depth of field (EDoF) from

300 mm to infinity. In the module the raw sensor outputs are digitally processed to obtain high contrast images. The

overall module is considered as an integrated computational imaging system (ICIS). The simulation results for

illustrative designs with different amount of spherical aberrations are provided and compared. Based on the results of

simulations we introduced the limiting value of the PSF Strehl ratio as the integral threshold criteria to be used during

EDoF lens optimization. A four-element standard lens was modified within the design constraints to achieve the EDoF

performance. Two EDoF designs created with different design methods are presented. The imaging modules were

compared in terms of Strehl ratios, limiting resolution, modulation frequencies at 50% contrast, and SNR. The output

images were simulated for EDoF modules, passed through the image processing pipeline, and compared against the

images obtained with the standard lens module.

Keywords: extended depth of field, lens optimization, image processing, integrated computational imaging system

1. INTRODUCTION

Today the overall quality of an image from a digital camera or a mobile phone camera is determined by the combined

performance of optics, imaging sensor and digital image processing. The intensive development of the CMOS imaging

technology, allowed creating high-resolution imaging module having pixel size as small as 1.75µm and less. When the

pixel size of a sensor is getting smaller, the lens has to have larger relative aperture to maintain and improve the SNR of

the system. One of the important characteristics of the camera, which affects the image quality, is its Depth-of-field

(DOF). In mobile phone cameras the DOF can be limited due to use of fast lens and small pixels. There have been a

number of publications addressing work on extending DOF in camera systems. Prior research includes such diverse

approaches as apodization by a weighted zone plate1, depth estimation2-5, light field photograhpy6, phase masks with

digital processing7-11. The weighted zone plate method allowed achieving a high Strehl ratio over large defocus region.

In this method the resolution could be further improved after applying digital image processing. Various depth

estimation methods are based on estimating high-order statistics (HOS) in an image, on edge detection and blur

measurement, on using multiple cameras to acquire images of a scene or on processing multiple defocused images. The

depth estimation method based on single image provides limited depth resolution. Also the accuracy of depth map could

be affected by scene contents. Use of multiple cameras or multiple defocused images would require more resources. In

the method based of light field photography the depth extension is achieved by inserting a microlens array between main

lens and sensor. Each microlens in the array produces an image of the exit pupil of the lens camera onto a unique area of

the sensor. The camera then extracts information about both horizontal and vertical parallax, which improves the

reliability of the depth estimates. The drawback of this camera is low overall resolution.

There have been several approaches to achieving extended depth of field using phase masks in combination with digital

processing. In such integrated computational imaging system, the optical transfer function (OTF) or point spread

function (PSF) is purposely blurred to become more invariant with object distance. The blurred images are then digitally

recovered using the invariant PSF. There is no light loss due to decreased aperture. Among these approaches, the

logarithmic asphere8, 10, 11 has circularly symmetry. The design of the logarithmic asphere is based on the Fermat’s

Principle which provides more invariant PSF. The logarithmic asphere profile could be expressed in terms of spherical

aberration which is easy to test.

*[email protected]; phone 1 408 660 2662; www.aptina.com

Novel Optical Systems Design and Optimization XI, edited by R. John Koshel, G. Groot Gregory,James D. Moore Jr., David H. Krevor, Proc. of SPIE Vol. 7061, 706103 · © 2008 SPIE

CCC code: 0277-786X/08/$18 · doi: 10.1117/12.795970

Proc. of SPIE Vol. 7061 706103-12008 SPIE Digital Library -- Subscriber Archive Copy

In this paper, we study how different optical design optimization methods affect EDoF performance of CMOS camera

when accounting for demosaicing and focus recovery (FR) post-processing. The overall image quality is characterized

against critical parameters of the optical system, such as spherical aberration, shape of PSF, and Strehl ratio. Two optical

design optimization methods for extending depth of field of ICIS are presented. The performance is compared against

that of a standard imaging module. A series of lenses were designed to introduce different amount of spherical

aberrations. Their performances are compared in terms of Strehl ratio, resolution before and after FR algorithm, MTF50

before and after FR, SNR before and after FR. Thresholds on Strehl ratios for imaging modules with 1.75µm pixel are

defined based on results of camera scene modeling (CSM) simulations. Further, we explore how modification of a

standard imaging lens for a specific 1.75µm 3 mega-pixel sensor extends the depth-of-field. Two EDoF designs are

presented and compared with the standard imaging module. The first EDoF lens is designed with logarithmic asphere

EDoF technology. The basic idea of logarithmic asphere is reviewed. The second EDoF lens is developed based on

optimization for achieving uniform PSFs over full field and range of object distances.

2. BASIC REQUIREMENTS TO PSF SHAPE AND STREHL RATIO

We used invariant PSF method to design lenses with EDoF properties over predefined range of object distances. The on-

axis PSF invariance was achieved by applying logarithmic asphere algorithm8, 10, 11. A series of lenses were generated

with the amount of spherical aberrations ranging from 0 to 6.824λ. The corresponding Strehl ratio was in the range from

1 to 0.1. All lenses have had the same first-order optics parameters values, such as F-number of 2.4, effective focal

length of 3.79 mm and half diagonal field of view of 30.5°. The PSF profile of each lens was used to generate simulated

image of a scene. The final image output accounted for optics, sensor response, and image processing. The simulated

results represent a real Bayer image output from the CMOS sensor with simulated camera noises added. This raw Bayer

image was demosaiced to generate the bitmap and further processed for FR and basic color pipeline. The digitally

recovered image is then evaluated for MTF, and SNR. The recovered image characteristics were measured for a series

of lenses with 3 mega-pixel 1.75µm pixel sensor with and without FR algorithm. The two representative PSFs for

lenses with different amount of 3rd-order spherical aberrations and defocus and with Strehl ratio of 0.1 and 1 are shown

in Figs. 1. No other aberrations were introduced into the designs.

Fig. 1(a) The PSF for an ideal diffraction- limited lens

without aberrations; the Strehl ratio is 1.

Fig. 1(b) The PSF for a lens with 6.824λ spherical

aberration and compensated defocus; the Strehl

ratio is 0.1.

The reference image produced with an ideal diffraction-limited lens (Strehl ratio of 1) (shown in Fig. 1 (a)) was

simulated for 1.75µm 3 mega-pixel sensor. It is shown in Fig. 2(a). The central part of the image was cropped on Fig.

2(b) to show details. The finest resolution bars in the upper left corner in Fig. 2(b) are smeared out due to aliasing which

is limited by sensor’s pixel size. We measure the MTF of this image using Imatest software. SNR is measured for the

third darkest gray patch in Fig. 2(b). From Fig. 2(b), we see that the finest resolution bar in the left upper corner is

smeared out due to aliasing. We notice that the red and blue channels of images in Figs. 2 have degraded after

demosaicing. Demosaicing procedure causes loss in image quality even when the diffraction-limited optics was used.

Proc. of SPIE Vol. 7061 706103-2

U U U

U...• U.U..

Fig. 2(a) The reference image simulated with an ideal lens. The lens has no aberrations; Strehl ratio of 1. The sensor has 3

million pixels, size 1.75µm.

Fig. 2(b) The cropped central part of the simulated image after demosaicing as shown in Fig. 2(a).

Additional Bayer images for a 1.75µm 3mega-pixel CMOS sensor were simulated using the lens PSFs with different

amount of spherical aberrations. These images were further processed with the FR and color pipeline algorithms. In the

FR algorithm the simulated PSFs were applied to restore the details of original scene. The modulation frequencies at

50% MTF (MTF50) along with the SNR values for demosaiced images before and after FR algorithm are presented in

Table I. MTF50 was measured using Imatest software.

From Table I it follows that the FR processing does improve the image contrast. The MTF50 is improved after FR

processing. But the cut-off frequency for a lens could not be improved by image restoration. When OTF has zeros at

frequencies less then Nyquist, the cut-off resolution is limited by optics instead of pixel. As the result, the FR

processing did not raise the cut-off frequencies of blurred images. FR amplified noise was depending on lens Strehl


ratio. The perfect lens with Strehl ratio of 1 has the best image quality. After considering cut-off resolution, image

contrast, and SNR of the processed image, we choose the Strehl ratio of 0.3 as the limiting threshold for EDoF design

with 1.75 µm CMOS sensor.

Table I. Comparison of modulation frequencies at 50% MTF (MTF50) and the SNR values for 1.75µm, 3 mega-pixel

CMOS sensor imaging modules with various amounts of spherical aberrations

3. OPTICAL DESIGN OPTIMIZATION FOR EDOF LENS

Further, we explore several optics optimization methods to be applied for designing high-resolution EDoF imaging

module. We’ve used the standard imaging lens as the starting design, and converted it into an EDoF lens. Two

examples of extended depth-of-field imaging lens are presented here. The first one is done with logarithmic asphere

technology. The second design is done with off-axis field optimization based on logarithmic asphere design. The focus

recovery algorithm allows achieving the best recovery of a scene image when the PSF stays constant over range of object

distances and the full field. For restoring high resolution images the Strehl ratio of invariant PSF’s should stay above the

threshold value as was described in section 2.

3.1 Standard imaging lens module

The first-order optics parameters for the standard lens are listed here: half field of view of 30.5°; F-number of 2.8;

maximum chief ray angle (CRA) is 28.4°; geometrical distortion of 1.7% (barrel); axial color is 3µm for spectrum range

from 0.43µm to 0.65µm; lateral color is 0.4µm. This lens was designed for a 1.75µm, 3 mega-pixel CMOS sensor. The

layout of this lens is shown in Fig. 3. The stop is located on the rear surface of the first lens element. This lens has

0.36λ of spherical aberration. All surfaces are standard or aspheric surfaces. We plotted the PSFs for object at 10meters,

65cm and 30cm in Figs. 4. Both PSFs’ shape and Strehl ratio strongly vary with object distances. This variation in PSF

leads to unrecoverable blurred images for out-of-focus objects.

Frequency for 50% MTF

(cys/mm)

SNR Amount of

spherical

aberration (λ)

Strehl

ratio

Before FR After FR Before FR After FR

0 1 101 - 30.1 -

1.93 0.5 81 91 28.5 27.3

2.53 0.3 86 89 28.5 26.3

2.70 0.25 66 89 30.1 26.3

2.90 0.2 66 90 28.1 23.3

6.82 0.1 32 54 27.0 19.3

Fig. 3 The layout of the standard imaging lens.


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MN' N'

Fig. 4(a) On-axis PSF for a

standard lens with object at

10meters. Strehl ratio is 0.879.

Fig. 4(b) On-axis PSF for a


65cm. Strehl ratio is 0.165.

Fig. 4(c) On-axis PSF for a


30cm. Strehl ratio is 0.071.

The plot of on-axis PSF Strehl ratio vs. object distance for this lens is shown in Fig. 5. The x-axis is object distance from

250mm to 10meters. The y-axis is the PSF Strehl ratio for an axial object. It is seen that the Strehl ratio drops below 0.3

when an object distance is less then 770mm.

The simulated images for scene objects positioned at 10meters, 65cm and 30cm are shown in Figs. 6(a), (b) and (c).

They are cropped from the whole field images. When object gets closer (shown in Figs. 6(b) and (c)), the second finest

resolution bar is not resolvable anymore. The poor image quality at 65cm and 30cm is within our expectation from PSFs

in Figs. 4(b) and 4(c). The Strehl ratio, spatial frequency for 50% MTF, and SNR for objects at 10meters, 65cm and

30cm are summarized in Table II. The SNR for object at 30cm is very high due to defocus blurring.

Fig. 5 The axial PSF Strehl ratio vs. object distance (from 250mm to 10meters) for a standard imaging lens.

Table II. Performance of a standard imaging module with 1.75µm sensor.

Object distance Strehl Ratio

(at 40% field height)

MTF50 Frequency

(cys/mm)

SNR

10meters 0.82 103 29.6

650mm 0.20 71 30.1

300mm 0.06 42 54.5


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3.2 Logarithmic asphere EDoF design method

The logarithmic asphere EDoF technology8, 10, 11 purposely blurs the point spread function so that PSF is invariant with

object distance. The logarithmic asphere lens has circularly symmetry with controlled continuous radial variation of

focal length. Each radial ring has one specific local focal length which provides a sharp focus of a specific object

distance on the detector plane. Therefore the images for objects within EDoF range are always sharply focused by one

specific ring of the lens and defocused by the other rings. The phase delay function )(ρφβ of a logarithmic asphere

EDoF lens is given by10

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Where t is the detector location; βα and βA are calculated with pre-determined EDoF range. )(ρφβ is the sum of the

phase transmission of an ideal diffraction-limited lens and the phase delay of the phase plate which provides EDoF. If

we expand the phase delay function of the phase plate into polynomial of 2ρ , it turns out the main terms are

4ρ and

6ρ which represent the 3rd-order and 5th-order spherical aberrations. With first-order optics parameters and pre-

determined EDoF range for object distance and Eq. (1), we could calculate the phase delay function of a logarithmic

asphere phase plate and convert it into surface profile. Before we calculate the phase delay function of the logarithmic

asphere phase plate, we specify which surface in the standard imaging lens to be modified. We know from the aberration

theory that modification on the stop surface does not change other third-order off-axis aberrations such as coma,

astigmatism, and Petzval curvature. Therefore we determine to modify the surface which is the closest to the stop. We

modify the rear surface of the first lens element, which is the stop surface as shown in Fig. 3, by minor change of the

aspheric coefficients for 4ρ ,

6ρ and 8ρ . The logarithmic asphere EDoF lens has the same first-order optics

parameters as the standard lens described in section 3.1. The geometric distortion is 1.7% (barrel). The axial color is

Fig. 6(a)

Fig. 6(b)

Fig. 6(c)

Fig. 6(a) 100% cropped simulated image for a standard lens imaging module with object at 10meters; Fig. 6(b) simulated

image for a standard lens with object at 65cm; Fig. 6(c) simulated image for a standard lens with object at 30cm. The

detector is a 1.75µm, 3mega-pixel CMOS sensor.


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3µm for spectrum from 0.43µm to 0.65µm. The lateral color is 0.35µm. This minor modification introduces -2.31λ of

spherical aberrations to the standard imaging lens. Therefore the logarithmic asphere EDoF lens has -1.95λ of spherical

aberrations. The on-axis PSFs for objects at 10meters, 65cm and 30cm are shown in Figs. 7. The Strehl ratios are 0.303,

0.570 and 0.191 for 10meters, 65cm and 30cm, respectively. Comparing Figs. 7 with Figs. 4, we see that as the object

distance changes, the logarithmic asphere EDoF lens has more consistent PSFs than the standard lens.

Fig. 7(a) On-axis PSF for

logarithmic sphere EDoF lens

with object at 10meters. Strehl

ratio is 0.303.

Fig. 7(b) On-axis PSF for


with object at 65cm. Strehl ratio

is 0.570.

Fig. 7(c) On-axis PSF for


with object at 30cm. Strehl ratio

is 0.191.

We simulated logarithmic asphere EDoF module images and applied the FR algorithm with the PSF at 65cm for objects

at 10meters, 65cm and 30cm. The cropped images are shown in Figs. 8. The second finest resolution bars on all three

images could be resolved. The image contrast on Fig. 8(b) is the best among the three images. The image quality

parameters are summarized in Table III for objects at 10meters, 65cm and 30cm. For extended depth-of field range of

300mm to infinity, there is no big loss in resolution. The contrast of images at 65cm and 10meters are comparable to the

contrast of a standard lens at best-focus distance. SNR are lower than standard lens due to the noise amplification by

digital processing.

Fig. 8(a)

Fig. 8(b)

Fig. 8(c)

Fig. 8(a) cropped simulated images for the logarithmic asphere EDoF lens at object distance 10meters; Fig. 8(b) simulated

image for object at 65cm; Fig. 8(c) simulated image for object at 30cm. The detector is a 1.75µm, 3mega-pixel CMOS sensor.


3.3 Optimization off-axis field performance in EDoF design

To further improve the off-axis field performance, we optimized the logarithmic asphere EDoF lens to obtain more

uniform point spread function over the entire field and over the range of object distances. We allowed the aspheric

coefficients, radius of curvatures and thickness of lenses to vary. The first-order optics parameters are constrained to be

the same as before. Geometrical distortion is 1.4% (barrel). The axial color is 4µm for spectrum range of 0.43µm to

0.65µm. The lateral color is 0.7µm. The maximum CRA is 29°. The amount of spherical aberration which is the

combination of 3rd-order, 5th-order and 7th-order spherical aberrations is -0.7λ. The lens layout is shown in Fig. 9. The

axial PSFs at 10meters, 65cm and 30cm are shown in Figs. 10. The variation in PSF is much less than the standard

imaging lens. The Strehl ratios vary from 0.259 to 0.385 for object distances from 30cm to infinity. The PSFs maintain

more uniform shape in comparison to the standard imaging lens.

Fig. 9 The lens layout for the optimized off-axis performance EDoF lens.

Fig. 10(a) On-axis PSF for

optimized off-axis performance

EDoF lens with object at

10meters. Strehl ratio is 0.385.

Fig. 10(b) On-axis PSF for


EDoF lens with object at 65cm.

Strehl ratio is 0.314.

Fig. 10(c) On-axis PSF for


EDoF lens with object at 65cm.

Strehl ratio is 0.259.

Table III. Performance of a logarithmic asphere EDoF imaging module with 1.75µm sensor.

Object distance Strehl Ratio

(at 40% field height)

MTF50 Frequency (cys/mm) SNR

10meters 0.27 100 21.8

650mm 0.45 102 22.0

300mm 0.23 61 21.9


The gradual improvements in the EDoF extension performance could be observed on Figs.11(a-c), comparing the

through-focus MTF plots prepared for the standard lens, the logarithmic asphere lens, and the lens with optimized off-

axis performance.

Fig. 11(a) Huygens through-focus MTF at Ny/4 (71.4cys/mm) for the standard imaging lens.

Fig. 11(b) Huygens through-focus MTF at Ny/4 (71.4cys/mm) for the logarithmic asphere EDoF lens.

Fig. 11 (c) Huygens through-focus MTF at Ny/4 (71.4cys/mm) for the EDoF lens with optimized off-axis performance.


The simulated image for the optimized lens in a 1.75µm, 3mega-pixel CMOS sensor module was processed through

focus recovery algorithm. The cropped part of the recovered image corresponding to 60% to 80% field heights is

compared with those for the ideal lens module and for the logarithmic asphere EDoF lens module in Fig. 12(c). The

object scene selected for simulation was the same scene as simulated in Fig. 2 (a). The object distance is equal to 10

meters.

Fig. 12(a) 100% cropped left

corner in the simulated image

for an ideal diffraction-limited

lens.

Fig. 12(b) 100% cropped left

corner in the recovered image

for the logarithmic asphere

EDoF lens.

Fig. 12(c) 100% cropped left

corner in the recovered image for

the optimized off-axis performance

EDoF lens.

The observation of images shown on Figs. 12(a-c) confirms that the ideal lens produced the best image quality. The off-

axis field performance of the improved off-axis EDoF lens is better than logarithmic asphere EDoF lens in terms of

resolution and contrast. The improved EDoF lens has the resolution and contrast comparable with the perfect lens, while

at the same time it produced more artifacts and noise. A better off-axis performance requires less variant PSF over field

or slowly varying PSF over field with PSF Strehl ratio to be above the 0.3 threshold level for good SNR. The

comparison of simulated images between the EDoF modules having lenses optimized with different design approaches

provides guidance on improving the lens design optimization procedures for better off-axis performance.

To compare the performance of the improved off-axis EDoF lens against that of the standard lens, we analyzed the 100%

cropped parts of images simulated for the standard lens, described earlier in section 3.1. The Figs. 13(a), (b) and (c) are

prepared for objects at 10meters, 65cm and 30cm, respectively. The imaging module has a 1.75µm, 3mega-pixel CMOS

sensor. In the images prepared for the standard lens imaging module we can see the how the resolution and contrast get

lost as the object moved closer to the lens. For comparison the images of the improved off-axis performance EDoF lens

are shown in Figs. 14. The sensor is the same as the one for the standard lens imaging module. When comparing images

on Figs. 13 and 14, it is visible that the image quality at 10meters is about the same for both modules. The image of the

EDoF module is getting slightly better than that of the standard lens module when object is at 65cm. The image of the

EDoF module is becoming superior to that for the standard lens module when object is at 30cm. The EDoF imaging

module extends the depth-of-field to 30cm or closer which gives 2x extension factor then that of the standard lens

module.

Proc. of SPIE Vol. 7061 706103-10

Fig. 13(a) standard lens with

object at 10meters.

Fig. 13(b) standard lens with

object at 65cm.

Fig. 13(c) standard lens with

object at 30cm.

4. CONCLUSION

It was demonstrated that the optical design for the high-resolution EDoF camera can be optimized from a standard lens

by introducing the proper amount of the spherical aberrations into optical elements, and simultaneously controlling the

uniformity of the Point Spread Function over the required range of object distances and over the full field. The Strehl

Ratio value of the PSF can be used as the one universal integral parameter for lens optimization. The image resolution

Fig. 14(a) EDoF lens with

improved off-axis performance

at 10meters.

Fig. 14(b) EDoF lens with


at 65cm.

Fig. 14(c) EDoF lens with


at 30cm.

Proc. of SPIE Vol. 7061 706103-11

and the overall quality are strongly affected by size and shape of a point spread function and Strehl Ratio. From the

analysis of the performance of the EDoF imaging module with 1.75µm 3 mega-pixel CMOS sensor, we concluded that

during optimization the lens PSF Strehl ratio should be kept above the 0.3 threshold value. We’ve designed two EDoF

lenses – one based on logarithmic asphere algorithm, and the other based on off-axis performance optimization. The

performances of both EDoF imaging modules were compared against that of a standard imaging module. The optimized

EDoF imaging modules allowed extending the depth-of-field to 30cm. As shown in Figs. 13 and 14, the images at object

distances 10meters, 65cm and 30cm taken with the EDoF imaging module look as good as the best-focused image taken

with the standard lens imaging module. An EDoF extension factor in the range of 2 to 3 was achieved.

5. ACKNOWLEDGEMENT

We are very thankful to our colleagues Dr. Brian Keelan, Dr. Dan Delescue and Dr. Junqing Chen for their suggestions

and supports. We are also very thankful to Dr. Wanli Chi at the Institute of Optics, University of Rochester for his great

ideas and suggestions.

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Proc. of SPIE Vol. 7061 706103-12

Optics optimization in high-resolution imaging module with extended depth of field

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