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The numerical recording and reconstruction of a color holographic image are achieved by using digital lensless Fourier transform holography. Firstly, for a color object, three monochromatic digital holograms with different wavelengths (red, green, blue) are recorded by a black-white CCD, respectively. Then the reconstructed monochromatic holographic images (red, green, blue) are adjusted to be same in size through padding digital holograms with zeros, and the corresponding digital color holographic image is acquired by accurately syncretizing the resized reconstructed monochromatic images. One of the advantages using lensless Fourier transform holography is that it can well assure the precise superposition of the reconstructed images. By applying median filtering technique and superposing the speckle fields with different distributions, the speckle noises are well suppressed and the quality of the digital color holographic image is greatly improved. This digital color holography with high quality of reconstruction effect would have potential applications on digital holographic display of color objects.
©2008 Optical Society of America
1. Introduction
The recording and reconstruction of a color holographic image by classical holography (using photographic plates and optical reconstruction) is usually rather complex and it is inconvenient for conservation, transmission and copy of the holograms recorded in a film or plate. In digital holography [1–5], the recording and reconstruction processes of the hologram are digital entirely and numerical disposals can be effectively implemented to improve the reconstruction results. The numerical reconstruction of a color object by using digital holography is presently a promising research subject. D. Alfieri and B. Javidi etc. did some elementary researches on this subject [6–7]. They recorded the holograms of a color object with two wavelengths by using off-axis Fresnel holography and acquired the color holographic image by padding zeros to the recorded holograms. However, the precise superposition of the reconstructed images from the holograms recorded at different distances couldn’t be well assured by using off-axis Fresnel holography, which would result in the illegibility of the boundary and the details of the fused holographic image at a certain extent. To solve this problem, we present an improved method, in which the digital holograms are recorded by using lensless Fourier transform holography [8–12].
2. Principles
As is known that, any color can be synthesized by the tricolor (red, green and blue). The reconstruction image of the digital hologram recorded with the monochromatic (red, green or blue) laser contains the corresponding color information of the recorded object, so we can get the color reconstruction image by synthesizing the three monochromatic (red, green and blue) reconstruction images. In order to obtain an accurately fused holographic image, the reconstructed images used for fusion should not only be identical in size but also be superposed precisely. Through simply padding zeros to the recorded digital holograms, the reconstructed image can be conveniently resized [13]. To assure that the reconstructed images of two holograms with different recording conditions have the identical size, the following equation should be satisfied
where N 1 2 and N 2 2 are the pixel number of the two digital holograms after being padded with zeros, λ 1 and λ 2 are the corresponding recording wavelengths, D 1 and D 2 are the corresponding recording distances, respectively.
In digital off-axis Fresnel holography, the transverse position of the reconstructed image on the reconstruction plane (relative to the center of the plane) is related to the angle (θ) between the object and the reference beams, the recording distance (D) and the direction of the irradiation beam used for numerical reconstruction. Assuming that the irradiation beam is perpendicular to the hologram plane, the position of the reconstructed image (L) can be calculated by L=Dtanθ. It is difficult to keep L constant when the recording distance D is changed because of the requirement on adjusting the angle θ precisely. The inconsistency of L will result in the inaccuracy when fusing the reconstructed images. The boundary and detail of the fused image will become blurred due to the displacement of the reconstructed images.
In digital lensless Fourier transform holography, the transverse position of the reconstructed image on the reconstruction plane is only determined by the distance between the object and the coplanar reference point source, but irrelative to the recording distance. Therefore the precise superposition of the reconstructed images for the holograms recorded at different distances can be well assured by using lensless Fourier transform holography. Moreover, compared with off-axis Fresnel holography, lensless Fourier transform holography has a lower requirement for the resolution of the recording medium and can make use of the bandwidth of CCD more efficiently in the recording process of the digital holograms, which is useful to improve the resolution of the reconstructed image [14].
3. Experiment results
The experimental set-up for recording digital lensless Fourier transform holograms is shown in Fig. 1. Three lasers with different wavelengths (λ 1=632.8nm, λ 2=532nm, λ 3=473nm) are used to record the digital holograms. They are arranged to allow propagating along the same paths either for the reference or the object beams. To satisfy the requirement of the lensless Fourier transform holography, the distance between the object and the CCD is equal to that between the reference point source and the CCD. A piece of ground glass is used to produce different diffuse illuminating light field. The digital holograms for red, green and blue laser are separately recorded by controlling the electronic shutters. The CCD used in experiment is a black-white type with 1392H×1040V pixels and 4.65µm×4.65µm pixel size.
Fig. 1. Experimental set-up for recording digital lensless Fourier transform hologram. M: mirror; BE: beam-expander; BS: beam-splitter.
The numerical reconstruction of digital lensless Fourier transform hologram is based on the Fresnel-transformation method (FTM), so the size of the reconstruction pixel (RP) could be calculated by the following equation:
where λ and D are the recording wavelength and distance of hologram, M (N) and Δx H (Δy H) are the pixel number and pixel size of CCD in the transverse (longitudinal) direction, respectively. To avoid the vision aberration of the reconstructed holographic image, the original digital hologram (1392H×1040V) is transformed to a square array (139 2H×1392V) by padding zeros and then numerically reconstructed. Figure 2 illustrates the color fusion process of the numerical reconstruction result of a piggy model, where Fig. 2(a) shows the red holographic image of the hologram recorded with wavelength of λ 1=632.8nm at distance of D 1=45cm, Fig. 2(b) shows the green holographic image of the hologram recorded with wavelength of λ 2=532nm at distance of D 2=46cm and Fig. 2(c) shows the blue holographic image of the hologram recorded with wavelength of λ 3=473nm at distance of D 3=47cm. According to the experimental parameters, it can be calculated that N 1:N 2:N 3=λ 1 D 1:λ 2 D 2:λ 3 D 3≈1.281:1.101:1. While the pixel number of the blue hologram is 1392H×1392V, the pixel number of the corresponding red (green) one after being padded with zeros should be 1784H×1784V (1532H×1532V), whose reconstruction result is shown in Fig. 2(d) (Fig. 2(e)). According to Eq. (2), the RP sizes of the three monochromatic holograms after padding with zeros are equal (RPR=RPG=RPB=34.3µm). Setup a three-layer zero matrix, then put the resized red, green and blue reconstruction result into the first, second and third layer of it, respectively. Color reconstruction image could be acquired by the display of the three-layer matrix. It is shown in Fig. 2(f) that the color holographic image has clear boundary and details because of the precise superposition of the reconstructed monochromatic image.
Fig. 2. Reconstruction results of a color piggy model by using digital lensless Fourier transform holography with multi-wavelengths. (a) λ 1=632.8nm, D 1=45cm; (b) λ 2=532nm, D 2=46cm; (c) λ 3=473nm, D 3=47cm; (d) Red appending-zeros hologram; (e) Green appending-zeros hologram (f) Color fusion of (c),(d) and (e).
4. Improvement of the reconstructed images
The quality of the reconstructed image is mainly affected by speckle noise. In order to improve the quality of the reconstructed image, we apply median filtering technique [15] and superpose the speckle fields with different distributions to suppress the speckle noise, as shown in Fig. 3. Figure 3(a) shows the original reconstructed image without any disposal. Figure 3(b) shows the corresponding disposal result obtained by applying median filtering technique. On the reconstructed image plane, the distributions of the reconstructed image are invariable, whereas the distributions of the speckle field change with the recording condition. Therefore, by superposing speckle fields with different distributions on the reconstructed image plane, the quality of the reconstructed image (corresponding superposition result) could be improved for the comparative reduction of speckle noise. By either changing the recording distance of the hologram or altering the diffuse light field used for illuminating the object, the speckle fields with different distributions can be obtained on the reconstructed image plane. Figure 3(c) and 3(d) show the corresponding superposition results of the speckle fields. In the experiment, the power of laser is invariable, so the intensity of the object beam and the intensity of the reference beam on the hologram-recording plane could also be considered as changeless. Therefore, the reconstructed images of different holograms have the same intensity and thus have equality when they are superposed for suppressing the speckle noise. Fig. 3(e) shows the final improvement result of the green reconstructed image obtained by the general use of these methods. It can be observed that the speckle noise is well suppressed and the quality of the holographic image is greatly improved.
Fig. 3. Improvement results of the reconstructed monochromatic image. (a) Without any disposal; (b) Median filtering; (c) Superposition of the speckle fields with different recording distance; (d) Superposition of the speckle fields with different illuminating light field; (e) General disposal.
Figure 4 displays the final digital color holographic image with high quality obtained by syncretizing the monochromatic holographic images improved through median filtering and superposition of the speckle fields with different distributions. Where, Fig. 4(a), 4(b) and 4(c) show the improved red, green and blue holographic images, respectively; Fig. 4(d) is the improved digital color holographic image, Fig. 4(e) is the part magnification of Fig. 4(d) and Fig. 4(f) shows the recorded color object.
Fig. 4. Improvement of the color holographic image. (a) Improved red holographic image; (b) Improved green holographic image; (c) Improved blue holographic image; (d) Fused color holographic image; (e) Part magnification of (d); (f) The recorded color object.
5. Conclusions
The reconstructed monochromatic images should not only be identical in size but also be superposed precisely in order to get an accurate digital color holographic image of a color object. The reconstructed monochromatic image can be conveniently resized through simple padding of the digital holograms with zeros. By using lensless Fourier transform holography, the precise superposition of the reconstructed images of digital holograms with different recording distances can be well assured. Based on the precise superposition of the reconstructed monochromatic images with the same size, we get the accurate digital color reconstruction image. By applying median filtering technique and superposing the speckle fields with different distributions, the speckle noises are well suppressed and digital color holographic image with high quality is obtained. It is expected that the quality of the digital color holographic image can be further improved by using the CCD with higher resolution, larger area and more efficient image processing technique. Although compared with photography or classical holography (a color image can be generated easier by photography and the reconstruction image obtained by classical holography can be easily viewed from different perspectives), the proposed digital color holography is not satisfying at some aspects due to the limitation of the CCD capability and the numerical reconstruction algorithm at present, it provides a reasonable method for getting accurate color image by using digital holography and thus would have potential applications on digital holographic display of color objects.
Acknowledgement
This work is supported by the Science Foundation of Aeronautics of China under grants No 2006ZD53042.
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