Abstract

The in-line holography has obvious advantages especially in wider spatial bandwidth over the off-axis holography. However, a direct current(DC)-noise and an unwanted twin image should be separated or eliminated in the in-line holography for a high quality reconstruction. An approach for suppressing the twin image is proposed by separating the real and twin image regions in the digital holography. Specifically, the initial region of real and twin images is obtained by a blind separation matrix, and the segmentation mask to suppress the twin image is calculated by nonlinear quantization from the segmented image. For the performance evaluation, the proposed method is compared with the existing approaches including the overlapping block variance and manual-based schemes. Experimental results showed that the proposed method has a better performance at the overlapped region of the real and twin images. Additionally, the proposed method causes less loss of real image than the overlapping block variance-based scheme. Therefore, we believe that the proposed scheme can be a useful tool for high quality reconstruction in the in-line holography.

© 2012 Optical Society of America

1. Introduction

The digital holography has been such a great issue these days because it can provide a three dimensional information corresponding to a real object [1, 2]. There is a practical subject coming from the optical configurations for off-axis and in-line holographies. The off-axis holography gives a better reconstruction with negligible noise than the in-line holography. However, the available bandwidth of off-axis holography is restricted by the tilted reference wave [35]. On the other hand, the in-line holography has obvious advantages in holographic reconstruction. One of the advantages is wider spatial bandwidth than that of the off-axis holography. However, its applicability is decreased due to the unwanted components during the reconstruction step. Therefore, it is still an open problem in in-line holography for a better numerical reconstruction. The typical unwanted components are twin image (conjugate image) and direct-current (DC) noise [4, 5]. To use wider spatial bandwidth in holographic reconstruction, twin image should be suppressed in in-line holographic configuration.

Numerical twin mage suppression has been researched by several approaches in in-line holography. The twin images suppression based on the segmented filter has been researched [46]. The segmented filter is calculated by the depth from focus(DFF) on in-focus twin image. To obtain the filter, the overlapping block variance of in-focus twin image is calculated to find the focused region [4, 5]. For a micro-object, the twin image suppression has been researched based on the iterations of propagation and back propagation [7, 8]. With the interaction, the binary function to suppress the twin image is calculated. Averaging multiple holographic reconstructions has been used to reduce a twin image based on a characteristic of statistically independent speckle field [9, 10]. However, the suppression by the multiple holographic reconstruction has the high complexity for the holographic reconstruction. Similarly, the twin image suppression with phase shifting interferometry(PSI) has been researched by capturing the multiple holograms with phase-shifting interferometer [1113].

In this work, an efficient way of generating the segmentation mask is presented to suppress the twin image in digital holography. Specifically, the real and twin image regions are separated by a blind separation matrix based on canceling coefficients, and the mask is created by applying the nonlinear quantization function to the output of the blind separation.

The proposed scheme is numerically explained and its practical procedure is experimentally described in Section 2. Next, experimental result is compared with those of the state-of-arts in Section 3. Finally, Section 4 summarizes the algorithm and concludes with some discussions.

2. Proposed approach: segmentation mask generation for suppressing twin image

In this section, the mask generation for a nonlinear segmentation is described. The complex amplitudes of an object and reference waves, respectively, in the digital holography are mathematically defined as

EO(x,y)=aO(x,y)eiφO(x,y)ER(x,y)=aR(x,y)eiφR(x,y)
where EO is an object wave with amplitude aO and phase φO, and ER is a reference wave with amplitude aR and phase φR. Therefore, a holographic fringe pattern, which is the interference pattern between the object and reference waves, is obtained as
I(x,y)=|EO(x,y)+ER(x,y)|2=aR2+aO2+EO(x,y)ER*(x,y)+ER(x,y)EO*(x,y)
where a symbol * denotes the complex conjugate, and the first two terms, which are the intensity of the object and reference waves respectively, contribute to a DC-noise.

To generate the segmentation mask, the fringe patten, which is released from [14], is reconstructed into in-focus real and twin images by the Fresnel approximation [3]. Then, to reduce the effect of DC-noise in the generation of segmentation mask, DC-noise in two images is simply suppressed by numerical high-pass filter [3, 15] as shown in Fig. 1.

 

Fig. 1 Input images for segmentation mask generation: (a) In-focus real image; (b) In-focus twin image. Note that the intensity values are doubled for better illustration.

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The procedure of the mask generation follows the block diagram as shown in Fig. 2. Specifically, two images which are in-focus real and twin images are inputted into the proposed scheme. Noise suppression [16, 17] is applied to suppress the speckle noise of two images. Next, real and twin images are separated by the blind separation matrix, which will be explained in Section 2.2, and the separated real image is quantized by a non-linear quantization function. To compensate the side effect occurred when low amplitude region at real image is filtered, inverse value of in-focus real image is generated for the inverse mapping. Then, the quantization function and the compensated image are combined to generate the nonlinear segmentation mask for the twin image suppression.

 

Fig. 2 Overall scheme to generate the nonlinear segmentation mask.

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2.1. preprocessing to reduce the noise effect

The in-focus real image iR1 after DC-noise reduction contains the focused real and unfocused twin images as illustrated in Fig. 1(a), while the in-focus twin image iT1 after reducing the noise contains the focused twin and unfocused real images as shown in Fig. 1(b). Speckle noise occurs both in two images due to the diffusion of coherent light by an optical rough surface [3]. Therefore, we employ the noise suppression scheme to reduce the effect of speckle noise for generating better segmentation mask. The speckle noise reduction has been researched based on multiple bandpass filters, PSI, and numerical filters including mean, Gaussian, and median filters [6, 16, 18]. The multiple bandpass filter and PSI require higher complexity than numerical filters, but a loss of edge information is caused by the numerical filters [19]. In particular, a bilateral filter [17] was used to suppress the noise with preserving the edge as a simple noise reduction scheme. A bilateral filter Hb consists of a set of spatial and range filters as

Hb=exp{12[d(ξ,x)σs]2}exp{12[δ(ξ,x)σr]2}
where ξ and x respectively denote the neighborhood center and a nearby point. d(ξ, x) and δ(ξ, x) indicate the Euclidean distance and the intensity difference, respectively, between ξ and x points. σs and σr represent the spatial and range parameters, respectively. The performance of bilateral filter is controlled by the spatial and range parameters. The spatial and range parameters, σs = 2.0 and σr = 0.5, are set, and the size of spatial filter is 3 × 3 in the proposed scheme. By applying it to two images, iR1 and iT1, two resultant images, iR2 and iT2, in which the speckle noise has been suppressed, are obtained as illustrated in Fig. 3.

 

Fig. 3 Speckle noise suppression by a bilateral filter: (a) In-focus real image; (b) In-focus twin image. Note that the intensity values are doubled for better illustration.

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2.2. Real and twin image separation by a blind separation matrix

After speckle noise suppression, a blind matrix is estimated for real and twin image separation. The in-focus real image contains both the focused real and unfocused twin images. Similarly, the in-focus twin image contains both the focused twin and unfocused real images. In order to build a simple model which can reflect the above conditions, an observed image should come both from the focused and unfocused images. Therefore, the in-focus real and twin images can be simply modeled by the combination of real and twin images, and the combination is numerically expressed by a mixing matrix A as

I=AS[iR2iT2]=[a11a12a21a22][sRsT]
where I is an observed vector that consists of the in-focus real iR2 and twin iT2 images, and S indicates the source vector which is composed of the real sR and twin sT images. The matrix A defines the mixing ratio of the real and twin images, in other words, models the relationship between the observed vector I and the source vector S.

To separate the real and twin images from the observation images, the blind separation matrix, which is the inverse matrix of A, is required, and the separated real and twin images can be rewritten by

S=A1I.
Therefore, the performance and complexity of the separation depend on the calculation of the blind separation matrix. Independent component analysis(ICA) based on neural network is one of the possible methods to obtain the matrix. However, it requires several iterations and operates under the independence or non-Gaussianity of sources [2022]. Hence, to obtain the matrix without an iteration and restrictions of the source, the blind and weighted separation matrix is computed from the canceling coefficients [21] in the separation step as
A1=[1a111a111a121a12][111c11c2]1
where a symbol ○ and cη represent Hadamard product and canceling coefficients, respectively.

For the coefficients, the two observed images are analyzed by the ratio in the frequency domain as

(iR2)(iT2)=a11SR(w)+a12ST(w)a21SR(w)+a22ST(w)
where a symbol ℱ represents the Fourier transform. If SR(w) is zero, then the first coefficient is calculated by c1 = a11/a21, and if ST (w) is zero, then the second coefficient is obtained from c2 = a12/a22. The blind separation matrix is calculated from the canceling coefficients in Eq. 6, and the in-focus real and twin images are separated into the regions of real and twin images as shown in Fig. 4, respectively. In practice, 3×3 block variance in ℱ(iR2)/ℱ(iT2) is calculated. Then, the first and the second smallest variances are used for the first and second canceling coefficients [21], respectively.

 

Fig. 4 Separated images by applying the weighted inverse matrix: (a) for an in-focus real image; (b) for an in-focus twin image.

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2.3. Segmentation mask generation by nonlinear quantization and compensation

Through the separation step, the region of real image is exposed in in-focus real image while the region of twin image is suppressed as illustrated in Fig. 4(a). The output of the separation for in-focus real image is used as an initial segmentation mask because the segmentation mask should pass the real image region and block the twin image region for the suppression of twin image. In order to divide the given image into real and twin regions properly, the critical threshold is calculated by the average of the initial mask as

T=int1N×MiNjMsR(i,j)
where int⌈·⌉ denotes a floor operation, and N and M are the row and column dimensions, respectively.

At the initial mask, a higher value than a threshold is fully passed while lower value than the threshold is filtered out to suppress twin image by the segmentation mask. However, in the overlapped region of real and twin images, a binary mask for separating them may be inappropriate, and it is possible to cause serious loss of real image data when the inaccurate mask is applied. Therefore, in the proposed scheme, a nonlinear quantization function is designed by using a sigmoidal nonlinearity [22], and defined as

Qt(x)=2×Db×[1+exp(x×2T×w)]1,{x:x(0,1,,T)}
where x, w, and Db represent an input sequence, the slope of the quantization function, and the bit depth of sR, respectively. Db is assigned to 255 for 8 bit images in the paper.

By the nonlinear quantization process, the lower region than the threshold is nonlinearly quantized while the higher region than the threshold is fully passed in the filtering. However, the side effect happens when low amplitude at real image is filtered out since the cut-off value for segmentation mask is decided by the threshold. Hence, the inverse map, which represents the low amplitude region in the in-focus real image at the mapping step, is calculated to compensate the side effect as

iM={1,ifiiR(i,j)>μ0,otherwisewhere,iiR(i,j)=1iR2(i,j)andμ=1N×MiNjMiiR(i,j).

According to the segmentation mask, the locations whose values in the map are equal to one are fully passed to reduce the side effect. And, the weights in the rest of the segmentation mask, where the mask values are not equal to one, are calculated by the nonlinear quantization function as

H={1,ifiM==1Qt[sR(i,j)],otherwise
Now, to suppress the twin image, the segmentation mask is multiplied with in-focus twin image [4, 5] as
iTs=iT2H
where a symbol · represents a pixel-by-pixel multiplication. Next, the segmented image iTs is delivered to the hologram plane by numerical propagation [4, 5]. Then, the holographic images are reconstructed by the Fresnel approximation [3] on the hologram. Procedure of the proposed scheme is summarized as Alg. 1.

Tables Icon

Algorithm 1:. Twin image suppression scheme by a nonlinear segmentation mask

3. Experiment

For the performance evaluation, the proposed approach is compared with the previous methods: the overlapping block variance-based and manually generated approaches. The fringe pattern [14] was used, and the pattern was reconstructed by the Fresnel approximation with a wave length λ =632.8nm and a pixel pitch Δ=6.8μm [14].

For the overlapping block variance-based method, block variance was calculated with 81×81 block size and the threshold was manually selected to generate the best performance segmentation mask. Similarly, for the manual-based approach, the best segmentation mask was generated manually. The generated segmentation masks are illustrated in Fig. 5. White and black regions of the segmentation mask denote one and zero values, respectively. Some regions of the twin and real images were selected by the overlapping block variance-based approach as shown in Fig. 5(a). The manually generated mask had the similar outline, zero values in the mask, with the twin image as illustrated in Fig. 5(b). The segmentation mask by the proposed scheme also had the similar outline with the twin image, and the most region of the twin image is filtered out by the mask while the most outside the twin image is passed by the segmentation mask as shown in Fig. 5(c). In the overlapped region of real and twin images, the real image was partially preserved and the twin image was partly suppressed as shown in Fig. 5(c). Note that the proposed segmentation mask had small spots on the real image region, but its spot size is much smaller than the size of spot by the overlapping block variance-based approach.

 

Fig. 5 Generated segmentation mask by each algorithm. From left to right: (a) Segmentation mask by overlapping block variance; (b) Manually generated mask; and (c) Segmentation mask from the proposed scheme.

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The in-focus twin image was multiplied with each of the segmentation masks on a pixel-by-pixel multiplication, and the segmented image was delivered to the hologram plane by numerical propagation [4, 5]. Then, the hologram was reconstructed by the Fresnel approximation [3]. The reconstructed images from the twin image suppression schemes were illustrated in Fig. 6. In Fig. 6(a), the twin image is appeared like a white cloud in the reconstructed image since twin image suppression was not considered. When the overlapping block variance-based segmentation mask was applied, the loss of real image and a little suppression of the twin image are caused as shown in Fig. 6(b). Similarly, the manually generated segmentation mask suppressed the twin image much at the cost of losing the real image in the overlapped region of real and twin images as shown in Fig. 6(c). In contrast, when the proposed mask was applied, twin image was suppressed well, and the loss of real image in the overlapped region is less compared with two methods as illustrated in Fig. 6(d). Also, small spots of the segmentation mask on the real image region had little influence on the real image because the size of spots was small, and the mask was nonlinearly quantized.

 

Fig. 6 Reconstructed digital holography images by the fresnel approximation for each algorithm. From top-left to bottom-right: (a) Result without twin image reduction; (b) Result with overlapping block variance-based segmentation mask; (c) Result with manually generated segmentation mask; and (d) Result with the proposed segmentation mask. Note that the intensity values are doubled for better illustration.

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In order to show the improvement effectively by the segmentation mask under the low speckle noise, bilateral filter [17] was finally applied both to the reconstructed images with and without the proposed twin-image suppression scheme. This procedure resulted in the two images of the speckle noise suppression as illustrated in Fig. 7. After reducing the speckle noise, the suppression of the twin image by the proposed scheme is much more clearly come into view. The intensity values of the twin image along the white solid line in Fig. 7 were plotted as shown in Fig. 8 for better observation. The black-dotted line and the gray-solid line indicate the intensity values of the reconstructed images without and with the proposed twin-image suppression scheme, respectively. It is easily seen that the intensity values with the proposed method were lower than those without the proposed method. Furthermore intensity value along the line was decreased from 31.71 to 21.48 on average by the proposed scheme.

 

Fig. 7 Speckle noise suppression results after applying a bilateral filter to reconstructed digital holography image. From left to right: (a) Result without twin image reduction; and (b) Result with the proposed segmentation mask. Note that the intensity values are doubled for better illustration.

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Fig. 8 Graphical comparison for the results without and with the proposed scheme in the solid line in Fig. 7(a) and 7(b). Black-dotted line and gray-solid line represent the crossover intensity values from without- and with-applying the proposed scheme, respectively.

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4. Conclusion

The scheme for generating a nonlinear segmentation mask was proposed by using a blind separation matrix obtained from the relation between in-focus real and twin images. The proposed method consisted of four blocks: noise suppression; separation; quantization; and mask generation. Specifically, speckle noise was suppressed first. Next, the region of real and twin images were modeled and separated by a blind separation matrix. Then, the separated image was nonlinearly quantized, and the segmentation mask was finally generated with the quantized image and the inverse map for the compensation of the side effects. In order to evaluate the proposed approach, performance comparison was conducted versus the existing algorithms, which are commonly used for twin image suppression in the digital holography. In the overlapped region of real and twin images, the proposed method had a less loss of real image than the compared methods and could even preserve the shape of real image. Additionally, the proposed method did not have a serious loss of the real image compared with the overlapping block variance-based scheme.

Therefore, we believe that the proposed scheme can be a useful tool for finding the regions of the real and twin images and suppressing the twin image for the high quality digital holography.

Acknowledgments

This work was supported by the IT R&D program of MKE/KEIT. [KI001810039169, Development of Core Technologies of Holographic 3D Video System for Acquisition and Reconstruction of 3D Information].

References and links

1. Y. Takaki and M. Yokouchi, “Speckle-free and grayscale hologram reconstruction using time-multiplexing technique,” Opt. Express 19, 7567–7579 (2011). [CrossRef]   [PubMed]  

2. C. S. Seelamantula, N. Pavillon, C. Depeursinge, and M. Unser, “Exact complex-wave reconstruction in digital holography,” J. Opt. Soc. Am. A 28, 983–992 (2011). [CrossRef]  

3. U. Schnars and W.P. Jüptner, “Digital recording and numerical reconstruction of hologram,” Meas. Sci. Technol. 13, 85–101 (2002). [CrossRef]  

4. C. P. McElhinney, J. B. McDonald, A. Castro, Y. Frauel, B. Javidi, and T. J. Naughton, “Depth-independent segmentation of macroscopic three-dimensional objects encoded in single perspectives of digital holograms,” Opt. Lett. 32, 1229–1231 (2007). [CrossRef]   [PubMed]  

5. C. McElhinney, B. M. Hennelly, L. Ahrenberg, and T. J. Naughton, “Removing the twin image in digital holography by segmented filtering of in-focus twin image,” in Optics and Photonics for Information , Proc. SPIE 7072, 707208 (2008).

6. D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting 2010, 1–14 (2010). [CrossRef]  

7. G. Koren, F. Polack, and D. Joyeux, “Iterative algorithms for twin-image elimination in in-line holography using finite-support constraints,” J. Opt. Soc. Am. A 10, 423–433 (1993). [CrossRef]  

8. L Denis, C Fournier, T Fournel, and C Ducotter, “Numerical suppression of the twin image in in-line holography of a volume of micro-objects,” Meas. Sci. Technol. 19, 1–10 (2008). [CrossRef]  

9. B. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin removal in digital holography using diffuse illumination,” Opt. Lett. 34, 3610–3612 (2009). [CrossRef]   [PubMed]  

10. D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin suppression in digital holography by mean of speckle reduction,” In Proceedings China-Ireland International Conference on Information and Communications Technologies, (Kildare, Ireland, 2009), 237–240.

11. J. Schwider, “Phase shifting interferometry: reference phase error reduction,” Appl. Opt. 28, 3889–3892 (1989). [CrossRef]   [PubMed]  

12. J. Hahn, H. Kim, S. Cho, and B. Lee, “Phase-shifting interferometry with genetic algorithm-based twin image noise elimination,” Appl. Opt. 47, 4068–4076 (2008). [CrossRef]   [PubMed]  

13. T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012). [CrossRef]  

14. V. L. Tuft, HoloVision 2.2 User’s manual (http://www2.edge.no/projects/holovision/doc/holovision221manual.pdf, 2001). [PubMed]  

15. H. Cho, J.K. Woo, D. Kim, S. Shin, and Y. Yu, “DC suppression in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers,” Opt. & Laser Tech. 41, 741–725 (2009). [CrossRef]   [PubMed]  

16. J. Maycock, B. M. Hennelly, J. B. McDonald, Y. Frauel, A. Castro, B. Javidi, and T. J. Naughton, “Reduction of speckle in digital holography by discrete Fourier filtering,” J. Opt. Soc. Am. A 24, 1617–1622 (2007). [CrossRef]  

17. C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of 6th IEEE International Conference on Computer Vision (IEEE, 1998), 839–846.

18. J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. 3, 289–294 (1971). [CrossRef]  

19. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Pearson, 2010).

20. J. V. Stone, Independent Component Analysis (MIT Press, 2004).

21. F. Abrard and Y. Deville, “A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources,” Signal Processing 85, 1389–1403 (2005). [CrossRef]  

22. T. K. Moon, Mathematical Methods and Algorithms for Signal Processing (Prentice hall, 2009).

References

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  • |
  • |

  1. Y. Takaki and M. Yokouchi, “Speckle-free and grayscale hologram reconstruction using time-multiplexing technique,” Opt. Express 19, 7567–7579 (2011).
    [Crossref] [PubMed]
  2. C. S. Seelamantula, N. Pavillon, C. Depeursinge, and M. Unser, “Exact complex-wave reconstruction in digital holography,” J. Opt. Soc. Am. A 28, 983–992 (2011).
    [Crossref]
  3. U. Schnars and W.P. Jüptner, “Digital recording and numerical reconstruction of hologram,” Meas. Sci. Technol. 13, 85–101 (2002).
    [Crossref]
  4. C. P. McElhinney, J. B. McDonald, A. Castro, Y. Frauel, B. Javidi, and T. J. Naughton, “Depth-independent segmentation of macroscopic three-dimensional objects encoded in single perspectives of digital holograms,” Opt. Lett. 32, 1229–1231 (2007).
    [Crossref] [PubMed]
  5. C. McElhinney, B. M. Hennelly, L. Ahrenberg, and T. J. Naughton, “Removing the twin image in digital holography by segmented filtering of in-focus twin image,” in Optics and Photonics for Information, Proc. SPIE  7072, 707208 (2008).
  6. D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting 2010, 1–14 (2010).
    [Crossref]
  7. G. Koren, F. Polack, and D. Joyeux, “Iterative algorithms for twin-image elimination in in-line holography using finite-support constraints,” J. Opt. Soc. Am. A 10, 423–433 (1993).
    [Crossref]
  8. L Denis, C Fournier, T Fournel, and C Ducotter, “Numerical suppression of the twin image in in-line holography of a volume of micro-objects,” Meas. Sci. Technol. 19, 1–10 (2008).
    [Crossref]
  9. B. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin removal in digital holography using diffuse illumination,” Opt. Lett. 34, 3610–3612 (2009).
    [Crossref] [PubMed]
  10. D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin suppression in digital holography by mean of speckle reduction,” In Proceedings China-Ireland International Conference on Information and Communications Technologies, (Kildare, Ireland, 2009), 237–240.
  11. J. Schwider, “Phase shifting interferometry: reference phase error reduction,” Appl. Opt. 28, 3889–3892 (1989).
    [Crossref] [PubMed]
  12. J. Hahn, H. Kim, S. Cho, and B. Lee, “Phase-shifting interferometry with genetic algorithm-based twin image noise elimination,” Appl. Opt. 47, 4068–4076 (2008).
    [Crossref] [PubMed]
  13. T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
    [Crossref]
  14. V. L. Tuft, HoloVision 2.2 User’s manual ( http://www2.edge.no/projects/holovision/doc/holovision221manual.pdf , 2001).
    [PubMed]
  15. H. Cho, J.K. Woo, D. Kim, S. Shin, and Y. Yu, “DC suppression in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers,” Opt. & Laser Tech. 41, 741–725 (2009).
    [Crossref] [PubMed]
  16. J. Maycock, B. M. Hennelly, J. B. McDonald, Y. Frauel, A. Castro, B. Javidi, and T. J. Naughton, “Reduction of speckle in digital holography by discrete Fourier filtering,” J. Opt. Soc. Am. A 24, 1617–1622 (2007).
    [Crossref]
  17. C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of 6th IEEE International Conference on Computer Vision (IEEE, 1998), 839–846.
  18. J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. 3, 289–294 (1971).
    [Crossref]
  19. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Pearson, 2010).
  20. J. V. Stone, Independent Component Analysis (MIT Press, 2004).
  21. F. Abrard and Y. Deville, “A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources,” Signal Processing 85, 1389–1403 (2005).
    [Crossref]
  22. T. K. Moon, Mathematical Methods and Algorithms for Signal Processing (Prentice hall, 2009).

2012 (1)

T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

2011 (2)

2010 (1)

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting 2010, 1–14 (2010).
[Crossref]

2009 (2)

B. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin removal in digital holography using diffuse illumination,” Opt. Lett. 34, 3610–3612 (2009).
[Crossref] [PubMed]

H. Cho, J.K. Woo, D. Kim, S. Shin, and Y. Yu, “DC suppression in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers,” Opt. & Laser Tech. 41, 741–725 (2009).
[Crossref] [PubMed]

2008 (3)

L Denis, C Fournier, T Fournel, and C Ducotter, “Numerical suppression of the twin image in in-line holography of a volume of micro-objects,” Meas. Sci. Technol. 19, 1–10 (2008).
[Crossref]

J. Hahn, H. Kim, S. Cho, and B. Lee, “Phase-shifting interferometry with genetic algorithm-based twin image noise elimination,” Appl. Opt. 47, 4068–4076 (2008).
[Crossref] [PubMed]

C. McElhinney, B. M. Hennelly, L. Ahrenberg, and T. J. Naughton, “Removing the twin image in digital holography by segmented filtering of in-focus twin image,” in Optics and Photonics for Information, Proc. SPIE  7072, 707208 (2008).

2007 (2)

2005 (1)

F. Abrard and Y. Deville, “A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources,” Signal Processing 85, 1389–1403 (2005).
[Crossref]

2002 (1)

U. Schnars and W.P. Jüptner, “Digital recording and numerical reconstruction of hologram,” Meas. Sci. Technol. 13, 85–101 (2002).
[Crossref]

1993 (1)

1989 (1)

1971 (1)

J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. 3, 289–294 (1971).
[Crossref]

Abrard, F.

F. Abrard and Y. Deville, “A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources,” Signal Processing 85, 1389–1403 (2005).
[Crossref]

Ahrenberg, L.

C. McElhinney, B. M. Hennelly, L. Ahrenberg, and T. J. Naughton, “Removing the twin image in digital holography by segmented filtering of in-focus twin image,” in Optics and Photonics for Information, Proc. SPIE  7072, 707208 (2008).

Castro, A.

Cho, H.

H. Cho, J.K. Woo, D. Kim, S. Shin, and Y. Yu, “DC suppression in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers,” Opt. & Laser Tech. 41, 741–725 (2009).
[Crossref] [PubMed]

Cho, S.

Dainty, J. C.

J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. 3, 289–294 (1971).
[Crossref]

Denis, L

L Denis, C Fournier, T Fournel, and C Ducotter, “Numerical suppression of the twin image in in-line holography of a volume of micro-objects,” Meas. Sci. Technol. 19, 1–10 (2008).
[Crossref]

Depeursinge, C.

Deville, Y.

F. Abrard and Y. Deville, “A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources,” Signal Processing 85, 1389–1403 (2005).
[Crossref]

Ducotter, C

L Denis, C Fournier, T Fournel, and C Ducotter, “Numerical suppression of the twin image in in-line holography of a volume of micro-objects,” Meas. Sci. Technol. 19, 1–10 (2008).
[Crossref]

Finke, G.

T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting 2010, 1–14 (2010).
[Crossref]

Fournel, T

L Denis, C Fournier, T Fournel, and C Ducotter, “Numerical suppression of the twin image in in-line holography of a volume of micro-objects,” Meas. Sci. Technol. 19, 1–10 (2008).
[Crossref]

Fournier, C

L Denis, C Fournier, T Fournel, and C Ducotter, “Numerical suppression of the twin image in in-line holography of a volume of micro-objects,” Meas. Sci. Technol. 19, 1–10 (2008).
[Crossref]

Frauel, Y.

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Pearson, 2010).

Hahn, J.

Hennelly, B.

T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

Hennelly, B. M.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting 2010, 1–14 (2010).
[Crossref]

B. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin removal in digital holography using diffuse illumination,” Opt. Lett. 34, 3610–3612 (2009).
[Crossref] [PubMed]

C. McElhinney, B. M. Hennelly, L. Ahrenberg, and T. J. Naughton, “Removing the twin image in digital holography by segmented filtering of in-focus twin image,” in Optics and Photonics for Information, Proc. SPIE  7072, 707208 (2008).

J. Maycock, B. M. Hennelly, J. B. McDonald, Y. Frauel, A. Castro, B. Javidi, and T. J. Naughton, “Reduction of speckle in digital holography by discrete Fourier filtering,” J. Opt. Soc. Am. A 24, 1617–1622 (2007).
[Crossref]

D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin suppression in digital holography by mean of speckle reduction,” In Proceedings China-Ireland International Conference on Information and Communications Technologies, (Kildare, Ireland, 2009), 237–240.

Javidi, B.

Joyeux, D.

Jüptner, W.P.

U. Schnars and W.P. Jüptner, “Digital recording and numerical reconstruction of hologram,” Meas. Sci. Technol. 13, 85–101 (2002).
[Crossref]

Kelly, D. P.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting 2010, 1–14 (2010).
[Crossref]

B. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin removal in digital holography using diffuse illumination,” Opt. Lett. 34, 3610–3612 (2009).
[Crossref] [PubMed]

D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin suppression in digital holography by mean of speckle reduction,” In Proceedings China-Ireland International Conference on Information and Communications Technologies, (Kildare, Ireland, 2009), 237–240.

Kim, D.

H. Cho, J.K. Woo, D. Kim, S. Shin, and Y. Yu, “DC suppression in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers,” Opt. & Laser Tech. 41, 741–725 (2009).
[Crossref] [PubMed]

Kim, H.

Koren, G.

Kozacki, T.

T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting 2010, 1–14 (2010).
[Crossref]

Kujawinska, M.

T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting 2010, 1–14 (2010).
[Crossref]

Lee, B.

Manduchi, R.

C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of 6th IEEE International Conference on Computer Vision (IEEE, 1998), 839–846.

Maycock, J.

McDonald, J. B.

McElhinney, C.

C. McElhinney, B. M. Hennelly, L. Ahrenberg, and T. J. Naughton, “Removing the twin image in digital holography by segmented filtering of in-focus twin image,” in Optics and Photonics for Information, Proc. SPIE  7072, 707208 (2008).

McElhinney, C. P.

Michalkiewicz, A.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting 2010, 1–14 (2010).
[Crossref]

Monaghan, B. S.

Monaghan, D. S.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting 2010, 1–14 (2010).
[Crossref]

D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin suppression in digital holography by mean of speckle reduction,” In Proceedings China-Ireland International Conference on Information and Communications Technologies, (Kildare, Ireland, 2009), 237–240.

Moon, T. K.

T. K. Moon, Mathematical Methods and Algorithms for Signal Processing (Prentice hall, 2009).

Naughton, T. J.

Pandey, N.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting 2010, 1–14 (2010).
[Crossref]

B. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin removal in digital holography using diffuse illumination,” Opt. Lett. 34, 3610–3612 (2009).
[Crossref] [PubMed]

D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin suppression in digital holography by mean of speckle reduction,” In Proceedings China-Ireland International Conference on Information and Communications Technologies, (Kildare, Ireland, 2009), 237–240.

Pavillon, N.

Polack, F.

Schnars, U.

U. Schnars and W.P. Jüptner, “Digital recording and numerical reconstruction of hologram,” Meas. Sci. Technol. 13, 85–101 (2002).
[Crossref]

Schwider, J.

Seelamantula, C. S.

Shin, S.

H. Cho, J.K. Woo, D. Kim, S. Shin, and Y. Yu, “DC suppression in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers,” Opt. & Laser Tech. 41, 741–725 (2009).
[Crossref] [PubMed]

Stone, J. V.

J. V. Stone, Independent Component Analysis (MIT Press, 2004).

Takaki, Y.

Tomasi, C.

C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of 6th IEEE International Conference on Computer Vision (IEEE, 1998), 839–846.

Unser, M.

Welford, W. T.

J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. 3, 289–294 (1971).
[Crossref]

Woo, J.K.

H. Cho, J.K. Woo, D. Kim, S. Shin, and Y. Yu, “DC suppression in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers,” Opt. & Laser Tech. 41, 741–725 (2009).
[Crossref] [PubMed]

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Pearson, 2010).

Yokouchi, M.

Yu, Y.

H. Cho, J.K. Woo, D. Kim, S. Shin, and Y. Yu, “DC suppression in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers,” Opt. & Laser Tech. 41, 741–725 (2009).
[Crossref] [PubMed]

Zaperty, W.

T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

Appl. Opt. (2)

Int. J. Digital Multimedia Broadcasting (1)

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting 2010, 1–14 (2010).
[Crossref]

J. Disp. Technol. (1)

T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

J. Opt. Soc. Am. A (3)

Meas. Sci. Technol. (2)

U. Schnars and W.P. Jüptner, “Digital recording and numerical reconstruction of hologram,” Meas. Sci. Technol. 13, 85–101 (2002).
[Crossref]

L Denis, C Fournier, T Fournel, and C Ducotter, “Numerical suppression of the twin image in in-line holography of a volume of micro-objects,” Meas. Sci. Technol. 19, 1–10 (2008).
[Crossref]

Opt. & Laser Tech. (1)

H. Cho, J.K. Woo, D. Kim, S. Shin, and Y. Yu, “DC suppression in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers,” Opt. & Laser Tech. 41, 741–725 (2009).
[Crossref] [PubMed]

Opt. Commun. (1)

J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. 3, 289–294 (1971).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Optics and Photonics for Information (1)

C. McElhinney, B. M. Hennelly, L. Ahrenberg, and T. J. Naughton, “Removing the twin image in digital holography by segmented filtering of in-focus twin image,” in Optics and Photonics for Information, Proc. SPIE  7072, 707208 (2008).

Signal Processing (1)

F. Abrard and Y. Deville, “A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources,” Signal Processing 85, 1389–1403 (2005).
[Crossref]

Other (6)

T. K. Moon, Mathematical Methods and Algorithms for Signal Processing (Prentice hall, 2009).

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Pearson, 2010).

J. V. Stone, Independent Component Analysis (MIT Press, 2004).

D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin suppression in digital holography by mean of speckle reduction,” In Proceedings China-Ireland International Conference on Information and Communications Technologies, (Kildare, Ireland, 2009), 237–240.

C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of 6th IEEE International Conference on Computer Vision (IEEE, 1998), 839–846.

V. L. Tuft, HoloVision 2.2 User’s manual ( http://www2.edge.no/projects/holovision/doc/holovision221manual.pdf , 2001).
[PubMed]

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Figures (8)

Fig. 1
Fig. 1 Input images for segmentation mask generation: (a) In-focus real image; (b) In-focus twin image. Note that the intensity values are doubled for better illustration.
Fig. 2
Fig. 2 Overall scheme to generate the nonlinear segmentation mask.
Fig. 3
Fig. 3 Speckle noise suppression by a bilateral filter: (a) In-focus real image; (b) In-focus twin image. Note that the intensity values are doubled for better illustration.
Fig. 4
Fig. 4 Separated images by applying the weighted inverse matrix: (a) for an in-focus real image; (b) for an in-focus twin image.
Fig. 5
Fig. 5 Generated segmentation mask by each algorithm. From left to right: (a) Segmentation mask by overlapping block variance; (b) Manually generated mask; and (c) Segmentation mask from the proposed scheme.
Fig. 6
Fig. 6 Reconstructed digital holography images by the fresnel approximation for each algorithm. From top-left to bottom-right: (a) Result without twin image reduction; (b) Result with overlapping block variance-based segmentation mask; (c) Result with manually generated segmentation mask; and (d) Result with the proposed segmentation mask. Note that the intensity values are doubled for better illustration.
Fig. 7
Fig. 7 Speckle noise suppression results after applying a bilateral filter to reconstructed digital holography image. From left to right: (a) Result without twin image reduction; and (b) Result with the proposed segmentation mask. Note that the intensity values are doubled for better illustration.
Fig. 8
Fig. 8 Graphical comparison for the results without and with the proposed scheme in the solid line in Fig. 7(a) and 7(b). Black-dotted line and gray-solid line represent the crossover intensity values from without- and with-applying the proposed scheme, respectively.

Tables (1)

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Algorithm 1: Twin image suppression scheme by a nonlinear segmentation mask

Equations (12)

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

E O ( x , y ) = a O ( x , y ) e i φ O ( x , y ) E R ( x , y ) = a R ( x , y ) e i φ R ( x , y )
I ( x , y ) = | E O ( x , y ) + E R ( x , y ) | 2 = a R 2 + a O 2 + E O ( x , y ) E R * ( x , y ) + E R ( x , y ) E O * ( x , y )
H b = exp { 1 2 [ d ( ξ , x ) σ s ] 2 } exp { 1 2 [ δ ( ξ , x ) σ r ] 2 }
I = A S [ i R 2 i T 2 ] = [ a 11 a 12 a 21 a 22 ] [ s R s T ]
S = A 1 I .
A 1 = [ 1 a 11 1 a 11 1 a 12 1 a 12 ] [ 1 1 1 c 1 1 c 2 ] 1
( i R 2 ) ( i T 2 ) = a 11 S R ( w ) + a 12 S T ( w ) a 21 S R ( w ) + a 22 S T ( w )
T = int 1 N × M i N j M s R ( i , j )
Q t ( x ) = 2 × D b × [ 1 + exp ( x × 2 T × w ) ] 1 , { x : x ( 0 , 1 , , T ) }
i M = { 1 , if i i R ( i , j ) > μ 0 , otherwise where , i i R ( i , j ) = 1 i R 2 ( i , j ) and μ = 1 N × M i N j M i i R ( i , j ) .
H = { 1 , if i M = = 1 Q t [ s R ( i , j ) ] , otherwise
i T s = i T 2 H

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