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We present experimental results with binary amplitude Fresnel lens arrays and binary phase Fresnel lens arrays used to implement integral imaging systems. Their optical performance is compared with high quality refractive microlens arrays and pinhole arrays in terms of image quality, color distortion and contrast. Additionally, we show the first experimental results of lens arrays with different focal lengths in integral imaging, and discuss their ability to simultaneously increase both the depth of focus and the field of view.
©2005 Optical Society of America
1. Introduction
Integral Imaging (II) is a 3D display technique which provides a full parallax stereoscopic view without additional glasses. To record the information of a 3D object, a microlens array in conjunction with a high resolution camera is used. Due to a different position of each microlens with respect to the imaged object, multiple perspectives of the 3D object can be imaged onto a CCD chip (Fig. 1). The recorded image that contains elemental images from each microlens can be electronically transferred and then reconstructed using a high resolution spatial light modulator in conjunction with another microlens array (Fig. 2),
Since Integral Photography has first been proposed by Lippmann [1], many techniques to increase the image depth [2–4] or the field of view [5–7] were investigated. Recently a method using a single non-uniform lens array was suggested by Jang et al. [8] to increase both parameters at the same time. To demonstrate the working principle a lens array with locally varying focal lengths had to be fabricated. There are different approaches to realize lens arrays using refractive, diffractive or hybrid lens designs [9]. Refractive lenslets can be fabricated using ultra-precise CNC machines, photoresist molding, hot embossing or ion-exchange techniques [10] to produces micro lenslet arrays [11–14] for integral imaging. Diffractive lenslets can be fabricated using direct laser or e-beam writing as well as mask techniques with binary or gray tone masks [11–12]. Because of the complex fabrication process of multi-focus refractive and multi-level diffractive lens arrays, we decided to first investigate binary Fresnel lens arrays. The target was to investigate their performance in terms of resolution, chromatic aberrations and image contrast and to verify if binary Fresnel lens arrays with multi-foci can be used in integral imaging systems. Other applications and systems to improve II performance have been proposed [15–19].
2. Design of a multi focus Fresnel lens array
The Fresnel lens arrays used in the experiments have been designed to generate 4 image planes, which are close enough to each other to generate a sharp reconstructed 3D image with an increased object depth. For this purpose, a lens array with 4 sets of lenses was used. To determine the focal lengths fi and the lens diameters, different considerations had been taken into account. The 3D image resolution is given by the number of lenses in x and y direction. The number of perspectives (angular resolution) in which the 3D object can be seen is given by the number of CCD pixels within one unit cell, which size is limited by the lens diameter and the lenses pitch. To fit the lens array grid to the LCD display grid and to realize a good spatial and angular resolution the diameter of all Fresnel lenses have been set to d=1.01mm. To realize a large field of view, the focal length of the microlens array should be chosen as small as possible. Due to the available fabrication tool set and the limits of the processes (writing, developing, etching) the minimum structure size was estimated to be 9 µm. Therefore, the width of the smallest Fresnel zone was set to 9 µm which lead to a minimum focal length of f1=15 mm at λ=633 nm.
To calculate the other three focal lengths, let us consider the lenslet is positioned at z=0, the position of the LCD display is at -g and the lenslet image plane is located at Li. For a given focal length fi the distance g can be calculated using the lens law (small angle approximation) given by
To get an acceptable field of view we set L1=100 mm. The display has then to be placed at g=-17.65 mm. We define the depth of the 3D integral image as the depth of focus of the lenslet. Assuming that di/2Li≪1, were di is the diameter of a single Fresnel lens, the depth of focus can be calculated [8] as
To increase the depth of focus, we want to use four sets of lenses with increasing focal length. We decided to increase the distance between each image plane Li by the factor 1·Di to get a smooth overlap between neighboring image planes. Thus
The spot size si in the lenslets image plane is determined by the Rayleigh criteria and is given by
Thus the resolution Ri=1/si in lines/mm. For g=-17.65 mm and λ=633 nm table 1 shows the calculated focal lengths fi, the image plane positions Li, the calculated image depth Di and the resolution Ri at the diffraction limit. As can be seen, the image depth increases by a factor of 5.5 from 25.3 mm for a single focus lens array to 138.7 mm using a four focus lens array. To generate a clear 3D image with increased object depth, only one image plane at a time should be visible. Therefore a second LCD shutter display should be used as an electro-optical mask which blocks 3 of the 4 lens sets in a rotational manner. Because 3 of 4 lens sets are blocked, double the elemental image size can be used during recording and reconstruction, thus leading to a simultaneous increase of the field of view by a factor of 2.
Table 1. Parameters of the multi-focus Fresnel lens array (calculated for reconstruction)
3. Fabrication
Two Fresnel lens arrays, one made of chrome (amplitude lenslet) and one of photoresist (phase lenslet) and a pinhole array (diameter d=200 µm, pitch p=1.1 mm) have been fabricated using laser-lithography, photo-lithography and wet chemical etch techniques. The lenslet arrays were designed for a wavelength of λ=633 nm. To write the master masks, a laser lithography system with a writing spot size of 0.8 µm was used. The spot was generated using a blue laser diode module (λ=405 nm) and a high numerical aperture objective lens of N.A.=0.9. The electronically modulated laser beam exposes the photoresist on the master substrate that is moved by a high precision air-bearing stage with an increment of 20 nm. The most challenging fabrication task was the high local resolution in combination with the large array size, which had to be written at once in order to avoid further photolithographic steps which would increase fabrication tolerances. To keep the writing times below 3 days, we used an array size of 26.26×20.20 mm to place 26×20 Fresnel lenses (13×10 unit cells) on one substrate. To handle the large number of pixels without slowing down the write tool for data preparation, we used a binary writing mode, in which each unit cell (2020×2020 pixels) was written separately and a control script was used to place all 130 unit cells at the right position. Figure 3 shows a microscope picture of a fabricated Fresnel lens unit cell. The focal lengths for the four lenses are the ones calculated in table 1. Figure 4 shows a magnification of the outer Fresnel zones. As can be seen, the smallest zones with a width of 9 µm have sharp edges and show no significant defects.
4. Optical performance of Fresnel lens arrays in integral imaging
To study the optical performance of the fabricated arrays in integral imaging systems, recording and reconstruction experiments have been performed using white and red light illumination.
In a first experiment we investigated the imaging quality of the fabricated lens arrays by using one single Fresnel lens (d=1.01 mm) to image a LCD displayed character (No. 4, 56×56 pixel, 2.1×2.1 mm) onto a diffuser plate. The recorded images from the backside of the diffuser plate produced by (A) a phase Fresnel lens and (B) an amplitude Fresnel lens are shown in Fig. 5. As can be seen, both Fresnel lenses were capable of imaging the character.
Attention should be drawn to the good image reproduction of the phase Fresnel lens, although the contrast was lower then with the refractive microlens array. The contrast is reduced by light that is diffracted into higher diffraction orders. The diffraction efficiency η for a staircase Fresnel lens [13] with N phase levels is given by
For a binary Fresnel lens (N=2) the efficiency in the first order is thus 40.5%. Looking at the amplitude Fresnel lens the contrast is equal, although only 50% of light is transmitted through the chrome structure. Unfortunately, due to the strong zero order diffraction cased by the not fully opaque chrome layer, strong glare in the picture occurs.
5. Recording experiments
A die with a diameter of 10 mm was placed at a distance of g=-40 mm in front of the diffractive lens and the pinhole arrays and a high resolution digital camera (Sigma, 3.3 Megapixel) was used to record the elemental images in the lenslets image plane. For the refractive microlens array the distance g was set to -7 mm because of the shorter focal length. To image the large lenslets image plane on the smaller CCD chip we used a zoom lens with a magnification of 10:1. We first investigated the optical performance in terms of contrast and picture sharpness of all lens arrays under white light illumination using a halogen light source. Figure 6 shows a selected center area of the recorded integral images using (A) a high quality refractive micro lens array, (B) a diffractive phase Fresnel lens array, (C) a diffractive amplitude Fresnel lens array and (D) a pinhole array.
As can be seen, the picture sharpness and contrast vary significantly. Using the software Matlab the contrast has been determined to be 91.6% for the refractive microlens array, 67% for the diffractive phase Fresnel lens array, 46.5% for the diffractive amplitude Fresnel lens array and 92.5% for the pinhole array. The sharpest picture was produced by the refractive microlens array, followed by the phase Fresnel lens array. The amplitude Fresnel lens array showed a similar sharpness, but suffered from the lower contrast due to transmitted zero order light. The lower contrast of 25.5% of the phase binary Fresnel lens compared to the refractive micro lens comes from the multifocus properties of the binary Fresnel lens which produces unsharp higher order images (different focal planes) in the recording plane. The picture quality of the pinhole array was weak and limited due to the large pinhole diameter which was chosen to get more light through the aperture. Using a pinhole array, the transmitted light was 25 times lower than with a refractive lens array. The picture sharpness of the pinhole array is limited by the diffraction limit. For d=200 µm and a distance of Li=40 cm, the diffraction limit was calculated to be d airy=2.4 mm using the Rayleigh criteria from Eq. (4).
Fig. 6. White light recorded elemental images using (A) a refractive microlens array, (B) a diffractive phase Fresnel lens array, (C) a diffractive amplitude Fresnel lens array, (D) a pinhole array.
To study the influence of chromatic aberrations in Fig. 6, the sharpest die of each recording (A-D) of Fig. 6 has been chosen and separated into the fundamental colors red/green/blue. The resulting gray level pictures have then been transformed into a false color representation to increase the visibility of distortions. The extracted images for red, green and blue for each lens array are shown in Fig. 7. The contours of the dice, recorded with the refractive micro lens and the pinhole array, do not visibly change. For the Fresnel lens recorded dice we can see slight chromatic aberrations due to the 20 times stronger dispersion of diffractive lenses. The chromatic focus shift for a refractive lens is small [14] and can be described by
where c1 and c2 are the curvatures from the front and rear lens surfaces and n(λ) is the refractive index at a specific wavelength λ. The chromatic focus shift for a diffractive Fresnel lens with focal length f0 designed at wavelength λ 0 is given by
Let’s consider the fabricated diffractive Fresnel lens array. A lens array with f0=15mm designed for λ0=633 nm produces a sharp image at the image plane L0 when the object is illuminated with the design wavelength λ0. Using Eq. (1) at a fixed object-lenslet distance g=-40 mm the sharpest image plane is located at L0=24 mm. For other wavelengths the spot will smear out at this plane due to a chromatic focus shift. Using geometric analysis the spot size sd for a beam at wavelength λ in the image plane L0 is given by
where d is the diameter of a single Fresnel lens and L λ is the sharp image plane for a lens with focal length f λ.
Fig. 7. Visualized chromatic aberrations using color separation of white light recorded elemental images.
We also used a zoom lens to reduce the size of the real image by a factor of M=10. In a first approximation we assume that the zoom lens did not induce additional chromatic aberrations (achromatic lens system) but reduced the chromatic focus shift in the lenslet image plane with the same fraction as the picture size. Using Eq. (8) the spot size on the CCD chip can then be determined by S λ=s λ/M. The smallest spot size S633 on the CCD chip where no focus shift occurred has been calculated using the Rayleigh criteria. The spot sizes S400 and S800 have been calculated using the geometric intercept theorem. To determine the image plane position L we used g=-7 mm for the refractive lens array (f=5 mm) and g=-40 mm for the diffractive Fresnel lens array (f=15 mm) as used in the recording experiments. The evaluated results are shown in table 2. We also estimated the chromatic aberrations of a Fresnel lens array with shorter focal length (f=5 mm) to compare their performance with the refractive microlens array. Here we used g=10 mm, to avoid a virtual image plane due to the strong chromatic focus shift.
Table 2. Chromatic aberrations of refractive and diffractive lenses
As can be seen in table 2, the chromatic focus shift f=f633-f400 for a diffractive Fresnel lens with a focal length of f=5 mm is approximately 20 times larger than with a refractive microlens of the same focal length. We define the ratio Sratio=S400/S633 as a measure for the image blur which allows us to compare chromatic aberrations of different lens types and focal lengths. The fabricated Fresnel lens array (f=15 mm) had nearly the same Sratio as the refractive microlens array (f=5 mm), also the smallest spot size was approx. 3 times larger due to the longer focal length which slightly decreased the image sharpness. Comparing a Fresnel lens and microlenses with the same focal length f=5mm and diameter d=1 mm, we found that the Sratio for the Fresnel lens was approx. 4 times larger. Thus a 4 times larger blur out of the picture sharpness at white light applications has to be accepted for Fresnel lenses with 5mm focus length. To determine an acceptable spectral bandwidth for white light imaging applications with the fabricated Fresnel lens arrays (f=15 mm) we assume, that the spectral blur out described by parameter Sratio should not become larger than 10. Let us describe the spectral bandwidth as 2Δλ. Because a wavelength variation in both directions will cause the same image blur we can simplify equation (8) using equation (7) and replacing λ by λ0+Δλ to
Thus the parameter Sratio can be written as
and thus Δλ can be determined to be
For a focal length f 0=15 mm at a center wavelength λ0=633 nm the spectral bandwidth 2xΔλ for an acceptable image quality is then 293 nm. If the spectrum will be Gaussian distributed, the intensity of the blur out will also be Gaussian distributed and therefore the image will look sharper than with a homogeneous spectral source. For nearly monochromatic illumination, we would achieve the same picture sharpness although the contrast would be 30% lower.
To verify this assumption, we used a red color Hoya-R60 filter for object illumination to reduce the spectral bandwidth. The recording results using red light illumination are shown in Fig. 8. As expected, the picture sharpness increased due to the absence of chromatic aberrations. In Fig. 8(B) we can now see different planes of sharpness from the upper left to the lower right corner due to the different designed focal lengths of our Fresnel lenslets.
Fig. 8. Red light recorded elemental images using (A) a refractive microlens array, (B) a diffractive phase Fresnel lens array, (C) a diffractive amplitude Fresnel lens array, (D) a pinhole array.
6. Reconstruction experiments
A full integral image (Fig. 9) recorded with the fabricated diffractive phase Fresnel lens array under red light illumination was reconstructed with a small (17.8×13.3 mm) SVGA LC display. The display was illuminated from the back side using a collimated halogen source for white light and an expanded He-Ne laser beam (λ̣=633nm) for monochromatic reconstruction.
To reduce speckles from the He-Ne laser light during reconstruction, a rotating diffuser plate has been installed in front of the laser. Figure 10 shows a reconstructed picture using a phase Fresnel lens array 10(A) with speckle reduction and in 10(B) without speckle reduction. As can be seen, a significantly smoother intensity distribution could be achieved.
Fig. 9. Displayed integral image which was recorded using a phase Fresnel lens array under red light illumination.
To record the reconstructed object, the same 3 megapixel camera was used and placed z=2 m behind the lenslet. For better interpretation and visualization a diffuser plate was positioned in the reconstruction image plane. To avoid vignetting effects, we decided to use no zoom lens for reconstruction. We therefore placed the lens arrays directly in front of the LCD at correct position g and varied the displayed image size on the display to adapt the elemental image size to the lens diameter. Due to the small size of the SVGA display, only 17×13 lenses of each array could be utilized. The Fresnel lens arrays and the pinhole array were positioned g=-17.1 mm in front of the LCD and produced a sharp image at a distance of Li=409 mm, the refractive micro lens array was positioned at g=-5.5 mm and had its image plane at Li=58 mm behind the lenslet array. Figure 11 shows the reconstructed pictures for all four lens arrays using a white light illumination. Figure 11 shows the same experiments for red light (He-Ne laser) illumination.
Fig. 11. Reconstructed elemental images using white backlight display illumination with different lens arrays: (A) refractive micro lens array, (B) diffractive phase Fresnel lens array, (C) diffractive amplitude Fresnel lens array, (D) pinhole array.
The multiple images of the dice which can be seen in each picture represent different viewing angles which are visible as flipping effects if no diffuser plate is present. As can be seen, the refractive micro lens array and the phase Fresnel lens array show a good optical reconstruction of the dice. Because we used the phase Fresnel lens recorded II-picture, the reconstruction with the phase Fresnel lens array is even sharper than with the microlens array. The image reconstructed with the amplitude Fresnel lens array is similar sharp but suffers from the low contrast due to zero order stray light (central area) as shown in Figs 12(C) and 12(C). The reconstructed dice is marked by arrows for better recognition. For the pinhole array, a reconstruction of the dice was not possible.
Fig. 12. Reconstructed elemental images using red backlight display illumination with different lens arrays: (A) refractive micro lens array, (B) diffractive phase Fresnel lens array, (C) diffractive amplitude Fresnel lens array, (D) pinhole array.
A reconstructed image without a diffuser plate using red light illumination and a phase Fresnel lens array is shown in Fig. 13. The picture shows the reconstructed 3D dice in front and the rotating speckle reducer in the background. As can be seen, the dice shows no flipping effects within the camera’s field of view which was FOVCam=3.6°.
Fig. 13. 3D real image without a diffuser plate, reconstructed using the phase Fresnel lens array and red backlight illumination
7. Summary
A pinhole array (d=0.2 mm, pitch p=1 mm) and two binary Fresnel lens arrays (one phase and one amplitude) with locally varying focal length (d=1.01 mm, F=15.0-16.4 mm) have been fabricated using photolithographic techniques and tested within an Integral Imaging system. Their recording and reconstruction performance under white, color filtered and monochromatic light have been investigated in terms of resolution, contrast and chromatic aberrations. The results have been compared with the performance of a commercially available high grade refractive microlens array (d=1 mm, F=5 mm). To the best of our knowledge, this is the first experimental demonstration of phase Fresnel lens arrays and multifocus Fresnel lens arrays in Integral Imaging applications. It could be shown that binary phase and amplitude Fresnel lens arrays are suitable alternative for refractive microlens arrays although constrictions in the contrast and picture sharpness have to be accepted. During white light recording experiments the measured contrast within the recorded elemental images was 91.6% using the refractive microlens array, 67% using the phase Fresnel lens array, 46.5% using the amplitude Fresnel lens array and 92.5% for the pinhole array. Chromatic aberrations with the refractive microlens and pinhole array were neglectable. The chromatic aberrations of both diffractive Fresnel lens arrays could be made visible using RGB picture splitting. The image blur could be calculated to be 1.1 times larger than with the refractive microlens array. Using a diffractive Fresnel lens array with same focal length (F=5 mm) the image blur had been calculated to be 4 times larger. The picture resolution was calculated to be 130 lines/mm using the refractive microlens array and 43 lines/mm using the diffractive Fresnel lens arrays (3 times larger focal length). Both the refractive microlens array and the phase Fresnel lens array showed a transmission of over 90%. The amplitude Fresnel lens array showed a transmission of 42% but suffered from strong zero order diffraction. The pinhole array with a 25 times lower transmission and a calculated resolution of 0.4 lines/mm was not suitable for imaging.
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