Synthetic aperture digital holography by movement of object ∗ Yu Z ha ng , Xiaoxu Lü1, Yinlong Luo, Liyun Zhong, Canlin She Laser Institute of Kunming University of Science and Technology, Kunming, Yunnan, P.R.china, 650051 ABSTRACT Synthetic aperture technique can be used to improve the reconstruction image resolution of digital hologram. In this paper, a synthetic aperture digital holographic method is proposed. In the method, the recording of synthetic aperture digital hologram is carried out by means of object movement in one direction, and the reconstruction is achieved by cross-correlation synthesis technique. Compared to the digital holography without synthetic aperture technique, only a one-dimension movable bracket is added in the experimental setup. The recorded object fixed on the movable bracket is placed in Mach-Zehnder interferometer and moved along horizontal direction. For the purpose of aperture synthesis reconstructing, four sub-digital holograms have been recorded by a CCD camera. While recording, superposition area of about half pixels of single digital hologram size should be assured between the adjacent holograms in order to ensure that the sub-digital holograms are synthesized accurately. The experimental result shows that every horizontal line of the reconstruction image is distinct in the synthetic aperture digital hologram, but the transverse is unidentifiable in the images reconstructed from the single digital holograms. It can be seen obviously that compared to sub-digital hologram the reconstruction image resolution of synthetic aperture digital hologram is improved. Keywords: Holography, digital holography, hologram, aperture, synthetic aperture, reconstruction, resolution, CCD camera, cross-correlation, intensity correlation. 1. INTRODUCTION In recent years, along with the development of computer technology and highly sensitive and real-time CCD camera, a great step forward has been made in holography1-5. But for the small amount of pixels, the effective recording area is much minor compared to the traditional holographic recording material. This leads to low resolution of reconstruction image in digital holography. For little aberration optical system, the theoretical equation of resolution can be expressed as ∆θ = λ 1.22 / D (1) Where D, λ and ∆θ represent the diameter of entrance pupil, wavelength of the homogeneous light and the minimum angular resolution of the optical system respectively. ∗ E-mail address: [email protected]. 1E-mail address: [email protected]; phone: +86(0871)3304093; fax: +86(0871)3304093. Holography, Diffractive Optics, and Applications II, edited by Yunlong Sheng, 581 Dahsiung Hsu, Chongxiu Yu, Byoungho Lee, Proceedings of SPIE Vol. 5636 (SPIE, Bellingham, WA, 2005) · 0277-786X/05/$15 · doi: 10.1117/12.573772 From the equation (1), it can be seen obviously that when wavelength is chosen, the resolution of optical system is dependent on the size of its transmission aperture D without regard to the environment noise. Therefore, in digital holography when monochromatic coherent source is selected, the resolution is mainly determined by the diameter of CCD camera. But for a variety of limiting conditions, it is impossible to increase the CCD pupil infinitely. To improve the reconstruction image resolution of digital hologram without adding extra main equipment, the method to increase the equivalent pupil of CCD by synthetic aperture technique is proposed in this paper. Recently, several reports about synthetic aperture digital holography have appeared and some preliminary study achievements in resolution improvement of reconstructed image are showed in these reports. According to Le. Lierc and M. Gross6, the synthetic aperture used in phase-shifting digital holography is acquired by moving a two-dimension detector and the method is demonstrated both theoretically and experimentally. In the report of Jürgen H.Massig7, the synthetic aperture digital hologram is reconstructed from camera recordings at nine different positions. Binet and Colineau8 propose an active optical synthetic aperture-imaging system in which a phase-step setup is required and the aperture synthesis is executed in one direction by means of rotation of object. A synthetic aperture obtained by object translation in horizontal direction is proposed in this paper. No phase shifters are required, which results in a less complex setup. In this method, the illumination object wave front and the reference arriving at CCD target surface is unchanged all along; this will overcome the inhomogeneity of the approximate plane wave. 2. THE DISTRIBUTION OF COMPLEX OPTICAL FIELD ON RECORDING AND RECONSTRUCTION PLANE IN SYNTHETIC APERTURE DIGITAL HOLOGRAPHY The coordination system schematic of the optical arrangement is shown in Fig.1. Here and in what follows, the object and CCD plane are represented by x0 y0 and x y respectively and the distance between recording object and CCD camera is represented by character z. If complex amplitude of homogeneous plane reference light and diffracted field distribution of an arbitrary object point (x0, y0) on CCD target surface are represented by R(x, y) and O(x0, y0 ；x, y) Reference beam Beam splitter CCD Object y z x Z Computer x0 y0 xy Fig.1. Coordination system of object and hologram respectively, then the complex amplitude of the digital hologram in the CCD plane can be written as 582 Proc. of SPIE Vol. 5636 = + 2 I(x, y) |O(xO , yO ,x, y) R(x, y)| (2) = 2 + 2 + * + * |O(xO , yO ,x, y)| | R(x, y)| O(xO , yO,x, y)R (x, y) O (xO, yO, x, y)R(x, y) Where * is the complex-conjugate operator and I(x, y) represents the complex amplitude of optical field in CCD plane. Let it be supposed that the recording positions are 1、2、3、…….N. During the movement of object and sub-digital holograms recording, we choose the object center when it is in the first position as the origin of x0y0 coordinate and the ideal image point of object center in CCD plane in every recording position as the xy coordinate origin. It is easy to know that the zero point of xy plane is shifting with the movement of the object. When the recording object is in position n, an arbitrary object and hologram point coordinate are written as (xon, yon) and (x, y) respectively. Then the sub-digital hologram recorded in position n can be represented as follow = 2 + 2 + * + * ∈ In (x, y) |O(xon, yon;x, y)| | R(x, y)| O(xon, yon;x, y)R (x, y) O (xon, yon;x, y)R(x, y) x, y Sn (3) Where Sn is the area of sub-digital hologram in position n. Then the synthetic aperture digital hologram combined by sub-digital holograms can be expressed as N N = = [ 2 + 2 + * + * ] I(x, y) ∑In (x, y) ∑ |O(xon, yon; x, y)| | R(x, y)| O(xon, yon;x, y)R (x, y) O (xon, yon;x, y)R(x, y) n=1 n=1 x, y∈(S1∪S2∪S3．．．．．．∪Sn） (4) If the simulated reconstruction reference beam of sub-digital hologram and synthetic aperture digital hologram is the same as the recording plane reference wave ( Cn(x, y)=C(x, y)=R(x, y)), then the complex amplitude distribution of reconstruction optical field of the sub-digital hologram recorded in position n can be expressed as = An (x, y) I n (x, y)C n (x, y) = [ 2 + 2 + * + | O(xon , yon , x, y) | | R(x, y) | O(xon , yon , x, y)R (x, y) * ] ∈ O (xon , yon , x, y)R(x, y) C(x, y) x, y Sn (5) = 2 + 2 + | O(xon , yon , x, y) | R(x, y) | R(x, y) | R(x, y) 2 + * 2 | R(x, y) | O(xon , yon , x, y) O (xon , yon , x, y)R (x, y) The reconstruction optical field of synthetic aperture digital hologram is A(x, y) = I(x, y)C(x, y) N = [ 2 + 2 + * + * ] ∑|O(xon, yon;x, y)| | R(x, y)| O(xon, yon; x, y)R (x, y) O (xon, yon;x, y)R(x, y) R(x, y) n=1 N = { 2 + 2 + 2 + * 2 } ∑ |O(xon, yon; x, y)| R(x, y) | R(x, y)| R(x, y) O(xon, yon; x, y)| R(x, y)| O (xon, yon; x, y)R (x, y) n=1 N = ∑An (x, y) n=1 x, y∈(S1∪S2∪S3．．．．．．∪Sn) (6) From equation (6), a conclusion can be reached: if a plane reference beam same as the recording reference beam is Proc. of SPIE Vol. 5636 583 chosen to reconstruct the sub-digital holograms and the synthetic aperture hologram, the superposition of the sub-reconstruction optical fields is just the complex amplitude distribution of the synthetic aperture digital hologram reconstruction optical field. 3. THE RECORDING AND RECONSTRUCTION METHOD OF SYNTHETIC APERTURE DIGITAL HOLOGRAPHY 3.1 Recording The fundamental light path of synthetic aperture digital holography is the same as the ordinary digital holography. The only difference is while recording each sub-digital hologram, the relative position of digital hologram and CCD camera must be changed. If CCD camera is moved parallel to the hologram plane and the arrangement of optical system hold the line, the Sub-hologram 1 Sub-hologram 2 whole hologram will not be changed but the part of (a) Two adjacent sub-holograms hologram on the CCD target surface will be varied. The mentioned reports6-8 about synthetic aperture digital holography are all based on this. When the illumination and the reference beam are plane, on any plane perpendicular to the light propagation Template n direction, the intensity and phase are both constant n1 2 value. Therefore, if the recording object is moved in (b) Template taking and recognizing such a plan and CCD camera is positioned perpendicular to the hologram plan, the relative intensity and phase distribution of the whole digital hologram will not change.