- Email: [email protected]
DC suppression in in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers
ARTICLE IN PRESS Optics & Laser Technology 41 (2009) 741–745
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
DC suppression in in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers Hyungjun Cho a, Jong-Kwan Woo a, Doocheol Kim a, Sanghoon Shin b, Younghun Yu a, a b
Department of Physics, Cheju National University, Ara 1 Dong, Jeju 690-756, Republic of Korea AP & Tec, Haedang-dong, Seoul 135-539, Republic of Korea
a r t i c l e in fo
abstract
Article history: Received 27 August 2008 Received in revised form 30 December 2008 Accepted 6 January 2009 Available online 3 March 2009
A simple method has been developed to suppress the DC term in in-line digital holographic microscope images. The technique is based on the use of the average intensity of a variable number of pixels rather than a fixed number of pixels. The DC-suppression ratio is similar to that associated with the averaging method proposed by Kreis and Juptner, while the image quality resulting from the new method is higher. This method can potentially yield significant improvements in the quality of reconstructed images. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Digital holography DC suppression Image reconstruction
1. Introduction Holography records the phase modulation of light reflected or transmitted from an object on a photosensitive medium in the form of an interference pattern. A reference and an object beam are required and an interference pattern is generated as a result of the combination of the two beams. Previously, the interference patterns were recorded on film plates. However, CCD and CMOS technology are now widely used for image capture and computers are used for hologram reconstruction. Yaroslavskii et al. first proposed hologram reconstruction on the basis of numerical values in the 1970s, and Ounral and Scott used numerical reconstruction to measure the size of a particle after improving the reconstruction algorithm. This method of digital recording and reconstruction of a numerical hologram is known as digital holography. Digital holography provides many advantages. For example, it does not require any chemical processing as the reconstructed image can be observed easily on a computer monitor, and numerical data for the three-dimensional shapes of objects can be obtained. However, the image resolution is an order of magnitude lower than that of standard film holography, while the image quality is degraded by DC (zeroth-order diffraction) noise and twin images. There are two types of holography, known as ‘‘off-axis’’ and ‘‘in-line.’’ In off-axis holograms, the overlapping angle between the reference and object beam is limited to within a few degrees
Corresponding author. Tel.: +82 64 754 3518; fax: +82 64 756 3506.
E-mail address: [email protected] (Y. Yu). 0030-3992/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2009.01.001
because of the limitations of the CCD pixel resolution. In in-line holograms, the angle between the reference and object beams is zero, i.e., they are parallel to each other (Gabor hologram). In offaxis holograms, the zeroth-order diffraction beam and the real and imaginary images are distinct and image reconstruction is possible. However, this method has the disadvantage that only 14 of the effective CCD area can be used [1,2]. On the other hand, in the in-line hologram the entire CCD area can be used, and therefore in-line holography is technically superior to its off-axis counterpart, as it has a superior field of view and resolution [3]. However, the zeroth-order and twin images are inseparable [4–7]. There are two methods to eliminate the DC term. The first proposed by Takaki uses a phase-shifting method [8,9]. Its efficiency in eliminating twin images and DC suppression is very high. However, due to the use of phase-shifting devices this method is very sensitive to environmental disturbances and it is difficult to measure dynamic phenomena. In the other method, proposed by Kreis and Juptner, the DC term is eliminated by subtracting the average intensity from the full hologram frame [10]. This method is simple to implement and is insensitive to environmental disturbances. However, DC suppression using the ‘‘averaging’’ method is not satisfactory for in-line holography as the spatial frequency of the resulting holograms is significantly different between the outer regions and the center. To overcome these limitations, we present a new method. Instead of using the average intensity of the entire hologram, we use variable-pixel average intensity. This method can suppress the DC term effectively, and thus significantly enhance the resulting image quality.
ARTICLE IN PRESS 742
H. Cho et al. / Optics & Laser Technology 41 (2009) 741–745
2. Theoretical model
30
In the hologram-recording process, a plane reference wave (R) and a diffusively reflected object wave (O) interfere at the CCD surface. The hologram intensity is given by IH ðx; yÞ ¼ jRj2 þ jOj2 þ R O þ RO ,
(1)
where R* and O* are the complex conjugates of the reference and object waves, respectively. The digital hologram, IH(k,l), is the N N array resulting from two-dimensional sampling IH(x,y) by the CCD camera N=2 N=2 x y X X IH ðk; lÞ ¼ IH ðx; yÞrect ; dðx kDx; y lDyÞ, L L k¼N=2 l¼N=2
20 15 10
0 0
where l and d are the wavelength and the reconstruction distance, respectively. From Eq. (3), the Fresnel–Kirchhoff integral is equivalent to the Fourier transformation of the function IH(x,y)exp[ip(x2+y2)/ld] with spatial frequencies x and Z. For rapid numerical calculation, a discrete formulation of Eq. (3) involving a two-dimensional fast Fourier transformation (FFT) can be derived directly as follows: expði2pd=lÞ ip 2 exp Cðm; nÞ ¼ ðm2 Dx þ n2 DZ2 Þ ild dl ip 2 2 2 ðk Dx þ l Dy2 Þ FFT IH ðk; lÞ exp , (4) ld m;n where k, l, m, and n are integers in the range N/2pk,l,m,npN/2. The values of the sampling intervals in the observation plane (Dx,DZ) can be derived directly from Dx ¼ DZ ¼ (ld/NDx) ¼ (ld/ L). As C(m,n) is an array of complex numbers, we can obtain an amplitude-contrast image using the intensity
and a phase-contrast image by calculating the argument Im½Cðm; nÞ . cðm; nÞ ¼ arctan Re½Cðm; nÞ
25
5
(2)
where k and l are integers, L L is the area covered by the CCD chip, and Dx and Dy define the pixel size. In classical optical holography, the object wave can be reconstructed by illuminating the processed hologram with a plane wave, which must be similar to that used in the recording process. If we look through the hologram, we observe a virtual image. If a screen is placed at a distance d behind the hologram, a real image is projected onto it. Mathematically, the amplitude and phase distribution in the plane of the real image can be found from the Fresnel–Kirchhoff integral [1,2]. If a plane wave illuminates the hologram with an amplitude transmittance IH(x,y), the Fresnel–Kirchhoff integral yields a complex amplitude, C(x,Z), in the real image plane expði2pd=lÞ ip 2 exp Cðx; ZÞ ¼ ðx þ Z2 Þ ild dl Z Z ip 2 ðx þ y2 Þ IH ðx; yÞ exp ld i2p exp ðxx þ ZyÞ dx dy, (3) ld
Iðm; nÞ ¼ Re½Cðm; nÞ2 þ Im½Cðm; nÞ2 ,
Selected number of pixels
2.1. Hologram recording and reconstruction
(5)
(6)
2.2. DC suppression In Eq. (1), the first two terms lead to the DC term in the reconstruction process. The average intensity (IM) of all pixels of
500 1000 1500 Location of pixels (x)
2000
Fig. 1. The number of selected pixels used for intensity averaging as a function of location across the hologram.
the hologram matrix is IM ¼
1 N 1 X 1 NX
N2
IH ðkDx; lDyÞ.
(7)
k¼0 l¼0
The DC term can now be suppressed by subtracting this average intensity from the hologram, I0 ðkDx; lDyÞ ¼ IH ðkDx; lDyÞ IM ðkDx; lDyÞ.
(8)
The reconstruction of I0 (kDx,lDy) creates an image that is almost free of the zeroth-order term. Suppression of the DC term on the basis of the average-intensity method is similar to the application of a high-pass filter. The cutoff spatial frequency depends on the number of pixels used for calculating the average intensity of the selected pixels, see Fig. 1. When we select the larger number of pixels, the cutoff frequency increases. If we adopt a low cutoff frequency, the efficiency of the DC suppression is high, but there is significant loss of information in the reconstructed image. To prevent this loss while maintaining the DC suppression efficiency, we use a variable number of pixels. In conventional in-line digital holography, almost all low spatial frequencies are located close to the center of the hologram. Therefore, we use the various sizes of selected pixels for intensity averaging as a function of hologram location, as shown in Fig. 1. For example, we selected 30 pixels at the center of CCD (x ¼ 1024), while we selected 3 pixels at the outer CCD block (x ¼ 1 or 2048) as shown in Fig. 1.
3. Experimental setup and results Fig. 2 shows a schematic diagram of a transmission hologram microscope. The basic experimental setup is similar to that of a Mach—Zehnder-type interferometer. A 10 mW He–Ne laser is used as the light source and the objective lens of a microscope, ML, is used to expand the beam passing through the sample. We used neutral-density filters, VN, to obtain the maximum contrast of the interference patterns. A beam expander, BE, is used for the reference beam in the TEM00 mode. We used a CCD camera (Sony IPX4M15L) to record the holograms. The pixel size and the number of pixels are 7.4 mm 7.4 mm and 2048 2048, respectively. The CCD is located at a distance of 20 cm from the ML and the overlapping angle between the reference and objective rays is maintained at 01, thus leading to in-line holography. Fig. 3 shows (a) the hologram measured at a distance of 20 cm from the rear focal point of the objective lens, and (b) a
ARTICLE IN PRESS H. Cho et al. / Optics & Laser Technology 41 (2009) 741–745
Object M
ML
743
BS
O
CCD
R
VN
M
Laser BS
VN
BE
Fig. 2. Transmission-type digital holographic microscopy. VN: variable-density filter, BS: beam splitter, M: mirror, O: object wave, R: reference wave, BE: beam expander with spatial filter, ML: microscope objective lens.
Fig. 3. Hologram and reconstructed image with DC suppression: (a) hologram; (b) reconstructed image with twin-image elimination; (c) DC-suppressed image based on 3 3-pixel intensity averaging; and (d) DC-suppressed image based on intensity averaging using variable pixel numbers.
numerically reconstructed image at a distance of 75 cm from the CCD. The twin image is eliminated using the zero-padding method [11]. The Fresnel diffraction equation is used for numerical reconstruction of the images. As shown in Fig. 3(b), the bright central square region corresponds to the reconstructed zeroth-order diffraction image. Figs. 3(c) and (d) are the DC-suppressed images resulting from the ‘‘averaging’’ method. We used 3 3-pixel regions to calculate the average intensity in Fig. 3(c), and variable pixel numbers in Fig. 3(d). In Fig. 3(d) we used 10 10 pixels in the central part of the hologram, 7 7 pixels in the middle, and 3 3 pixels in the outer regions.
The DC-suppression ratio is defined as the ratio between the full intensity of the hologram and the intensity averaged over 80 80 pixels covering the central area of the reconstructed image. The DC-suppression ratios in Fig. 3(c) and (d) are similar, but the amount of information loss from the images is different. The image areas inside the dotted circles in Fig. 3(c) and (d) are different. From Fig. 3 we found that the DC-suppression ratios of the ‘‘average’’ and ‘‘variable-average’’ methods are similar, but the image quality is different. We could obtain better-quality images using the variable pixel number intensity-averaging method. Fig. 4 shows (a) a hologram, the grating pattern of which was measured at a distance of 20 cm from the rear focal point of the
ARTICLE IN PRESS 744
H. Cho et al. / Optics & Laser Technology 41 (2009) 741–745
Fig. 4. Hologram and DC-suppressed reconstructed images: (a) hologram; (b) DC-suppressed image after 3 3-pixel intensity averaging; and (c) DC-suppressed image using variable pixel number intensity averaging.
0.8
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N(30) A(3-10) A(3-30) A(10-30)
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Numbers of pixels used for averaging 0.18
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0.00
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400
500
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700
800
pixel
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Fig. 5. DC-suppression ratio and contrast: (a) DC-suppression ratio; (b) modulation transfer function; (c) gray level intensity of dotted line A in Figs. 4(b) and (c); and (d) gray level intensity of dotted line B in Figs. 4(b) and (c). The dotted and solid lines in panels (b) and (c) represent the results from the variable-pixel and the normal method, respectively.
objective lens, and (b, c) numerically reconstructed images at a distance of 75 cm from the CCD. Fig. 4(b) shows the DC-suppressed image using 3 3-pixel intensity averaging and Fig. 4(c) shows the DC-suppressed image using variable pixel numbers, as in Fig. 3(d). The images in Fig. 4(b) and (c) are different. We measured the gray level along the dotted lines in Fig. 4(b) and (c); the results are shown in Fig. 5(c) and (d).
Fig. 5(a) shows the DC-suppression ratio as a function of the number of pixels used for intensity averaging. Here, N(3) indicates that we used 3 3 pixels to calculate the average intensity, as suggested by Kreis and Juptner; A(3–10) indicates that we used 3 3 pixels in the outer regions of the hologram and 10 10 pixels in the central area to calculate the average intensity. Fig. 5(a) shows the DC-suppression ratio, which increases as the number of pixels used decreases. The suppression ratios from the method of
ARTICLE IN PRESS H. Cho et al. / Optics & Laser Technology 41 (2009) 741–745
Kreis and Juptner and the variable pixel number methods are similar. These results are reasonable as the averaging method is similar to the application of a high-pass filter. If we adopt a given cutoff frequency, higher frequencies are not influenced by the filter. Figs. 5(c) and (d) illustrate the measured gray levels along the dotted lines A and B in Fig. 4(b) and (c). From Fig. 5(c) and (d), it follows that the contrast of the gray level in the image reconstructed using the variable pixel number method is higher than that resulting from the ‘‘normal’’ (i.e., fixed number of pixels) averaging method. The contrast degrades rapidly in the central regions of the image based on the normal averaging method (solid lines in Fig. 5(c) and (d)). This degradation is caused by image information loss due to the averaging process. However, the variable pixel number averaging method does not degrade the image quality as much as the normal (fixed pixel number) averaging method. Fig. 5(b) shows the modulation transfer function (MTF) as a function of pixel number. The MTF also shows that we can obtain a higher quality DC-suppressed reconstructed image on the basis of the variable pixel number method.
4. Conclusions A simple method was developed to suppress the DC term in inline digital holographic microscopy images on the basis of the average intensity of variable instead of fixed numbers of pixels. The DC-suppression ratio is similar to that of the intensity-averaging method proposed by Kreis and Juptner, although the image quality in the new method is higher. As this new method is intrinsically simple and does not require any additional equipment, it is not sensitive to environmental disturbances and
745
can also be used for dynamic measurements. This new method can thus significantly improve the quality of reconstructed images.
Acknowledgments This study was supported by the Korean Ministry of Commerce, Industry, and Energy. A number of the researchers participating in this study are supported by a grant from the ‘‘Second-phase BK21 project.’’ References [1] Cuche E, Marquet P, Depeursinge C. Simultaneous amplitude-contrast and quantitative phase- contrast microscopy by numerical reconstruction of Fresnel off-axis holograms. Appl Opt 1999;38:6994–7001. [2] Cuche E, Marquet P, Depeursinge C. Spatial filtering for zero-order and twin image elimination in digital off-axis holography. Appl Opt 2000;39:4070–5. [3] Xu L, Peng X, Guo Z, Miao J, Asundi A. Imaging analysis of digital holography. Opt Express 2005;13:2444. [4] Goodman JW. In: Introduction to Fourier optics. 2nd ed. New York: McGraw Hill; 2005. [5] Schnars U, Juepther W. In: Digital holography. Heidelberg: Springer; 2005. [6] Denis L, Corinne F, Thierry F, Christophe D. Twin-image noise reduction by phase retrieval in in-line digital holography. Proc SPIE 2005;5914:148. [7] Depeursinge C. In: Digital holography applied to microscopy. USA: Springer; 2006. [8] Takaki Y, Kawai H, Ohzu H. Hybrid holographic microscopy free of conjugate and zero-order images. Appl Opt 1999;38:4990–6. [9] Yamaguchi I, Zhang T. Phase-shifting digital holography. Opt Lett 1998;23:1221–3. [10] Kreis T, Juptner WPO. Suppression of the DC term in digital holography. Opt Eng 1997;36:2357–60. [11] Cho H, Kim D, Shin S, Jang W, Son J, Yu Y. Twin-image elimination in an in-line digital holographic microscope. J Korean Phys Soc 2008;52:1031–5.
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
DC suppression in in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers Hyungjun Cho a, Jong-Kwan Woo a, Doocheol Kim a, Sanghoon Shin b, Younghun Yu a, a b
Department of Physics, Cheju National University, Ara 1 Dong, Jeju 690-756, Republic of Korea AP & Tec, Haedang-dong, Seoul 135-539, Republic of Korea
a r t i c l e in fo
abstract
Article history: Received 27 August 2008 Received in revised form 30 December 2008 Accepted 6 January 2009 Available online 3 March 2009
A simple method has been developed to suppress the DC term in in-line digital holographic microscope images. The technique is based on the use of the average intensity of a variable number of pixels rather than a fixed number of pixels. The DC-suppression ratio is similar to that associated with the averaging method proposed by Kreis and Juptner, while the image quality resulting from the new method is higher. This method can potentially yield significant improvements in the quality of reconstructed images. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Digital holography DC suppression Image reconstruction
1. Introduction Holography records the phase modulation of light reflected or transmitted from an object on a photosensitive medium in the form of an interference pattern. A reference and an object beam are required and an interference pattern is generated as a result of the combination of the two beams. Previously, the interference patterns were recorded on film plates. However, CCD and CMOS technology are now widely used for image capture and computers are used for hologram reconstruction. Yaroslavskii et al. first proposed hologram reconstruction on the basis of numerical values in the 1970s, and Ounral and Scott used numerical reconstruction to measure the size of a particle after improving the reconstruction algorithm. This method of digital recording and reconstruction of a numerical hologram is known as digital holography. Digital holography provides many advantages. For example, it does not require any chemical processing as the reconstructed image can be observed easily on a computer monitor, and numerical data for the three-dimensional shapes of objects can be obtained. However, the image resolution is an order of magnitude lower than that of standard film holography, while the image quality is degraded by DC (zeroth-order diffraction) noise and twin images. There are two types of holography, known as ‘‘off-axis’’ and ‘‘in-line.’’ In off-axis holograms, the overlapping angle between the reference and object beam is limited to within a few degrees
Corresponding author. Tel.: +82 64 754 3518; fax: +82 64 756 3506.
E-mail address: [email protected] (Y. Yu). 0030-3992/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2009.01.001
because of the limitations of the CCD pixel resolution. In in-line holograms, the angle between the reference and object beams is zero, i.e., they are parallel to each other (Gabor hologram). In offaxis holograms, the zeroth-order diffraction beam and the real and imaginary images are distinct and image reconstruction is possible. However, this method has the disadvantage that only 14 of the effective CCD area can be used [1,2]. On the other hand, in the in-line hologram the entire CCD area can be used, and therefore in-line holography is technically superior to its off-axis counterpart, as it has a superior field of view and resolution [3]. However, the zeroth-order and twin images are inseparable [4–7]. There are two methods to eliminate the DC term. The first proposed by Takaki uses a phase-shifting method [8,9]. Its efficiency in eliminating twin images and DC suppression is very high. However, due to the use of phase-shifting devices this method is very sensitive to environmental disturbances and it is difficult to measure dynamic phenomena. In the other method, proposed by Kreis and Juptner, the DC term is eliminated by subtracting the average intensity from the full hologram frame [10]. This method is simple to implement and is insensitive to environmental disturbances. However, DC suppression using the ‘‘averaging’’ method is not satisfactory for in-line holography as the spatial frequency of the resulting holograms is significantly different between the outer regions and the center. To overcome these limitations, we present a new method. Instead of using the average intensity of the entire hologram, we use variable-pixel average intensity. This method can suppress the DC term effectively, and thus significantly enhance the resulting image quality.
ARTICLE IN PRESS 742
H. Cho et al. / Optics & Laser Technology 41 (2009) 741–745
2. Theoretical model
30
In the hologram-recording process, a plane reference wave (R) and a diffusively reflected object wave (O) interfere at the CCD surface. The hologram intensity is given by IH ðx; yÞ ¼ jRj2 þ jOj2 þ R O þ RO ,
(1)
where R* and O* are the complex conjugates of the reference and object waves, respectively. The digital hologram, IH(k,l), is the N N array resulting from two-dimensional sampling IH(x,y) by the CCD camera N=2 N=2 x y X X IH ðk; lÞ ¼ IH ðx; yÞrect ; dðx kDx; y lDyÞ, L L k¼N=2 l¼N=2
20 15 10
0 0
where l and d are the wavelength and the reconstruction distance, respectively. From Eq. (3), the Fresnel–Kirchhoff integral is equivalent to the Fourier transformation of the function IH(x,y)exp[ip(x2+y2)/ld] with spatial frequencies x and Z. For rapid numerical calculation, a discrete formulation of Eq. (3) involving a two-dimensional fast Fourier transformation (FFT) can be derived directly as follows: expði2pd=lÞ ip 2 exp Cðm; nÞ ¼ ðm2 Dx þ n2 DZ2 Þ ild dl ip 2 2 2 ðk Dx þ l Dy2 Þ FFT IH ðk; lÞ exp , (4) ld m;n where k, l, m, and n are integers in the range N/2pk,l,m,npN/2. The values of the sampling intervals in the observation plane (Dx,DZ) can be derived directly from Dx ¼ DZ ¼ (ld/NDx) ¼ (ld/ L). As C(m,n) is an array of complex numbers, we can obtain an amplitude-contrast image using the intensity
and a phase-contrast image by calculating the argument Im½Cðm; nÞ . cðm; nÞ ¼ arctan Re½Cðm; nÞ
25
5
(2)
where k and l are integers, L L is the area covered by the CCD chip, and Dx and Dy define the pixel size. In classical optical holography, the object wave can be reconstructed by illuminating the processed hologram with a plane wave, which must be similar to that used in the recording process. If we look through the hologram, we observe a virtual image. If a screen is placed at a distance d behind the hologram, a real image is projected onto it. Mathematically, the amplitude and phase distribution in the plane of the real image can be found from the Fresnel–Kirchhoff integral [1,2]. If a plane wave illuminates the hologram with an amplitude transmittance IH(x,y), the Fresnel–Kirchhoff integral yields a complex amplitude, C(x,Z), in the real image plane expði2pd=lÞ ip 2 exp Cðx; ZÞ ¼ ðx þ Z2 Þ ild dl Z Z ip 2 ðx þ y2 Þ IH ðx; yÞ exp ld i2p exp ðxx þ ZyÞ dx dy, (3) ld
Iðm; nÞ ¼ Re½Cðm; nÞ2 þ Im½Cðm; nÞ2 ,
Selected number of pixels
2.1. Hologram recording and reconstruction
(5)
(6)
2.2. DC suppression In Eq. (1), the first two terms lead to the DC term in the reconstruction process. The average intensity (IM) of all pixels of
500 1000 1500 Location of pixels (x)
2000
Fig. 1. The number of selected pixels used for intensity averaging as a function of location across the hologram.
the hologram matrix is IM ¼
1 N 1 X 1 NX
N2
IH ðkDx; lDyÞ.
(7)
k¼0 l¼0
The DC term can now be suppressed by subtracting this average intensity from the hologram, I0 ðkDx; lDyÞ ¼ IH ðkDx; lDyÞ IM ðkDx; lDyÞ.
(8)
The reconstruction of I0 (kDx,lDy) creates an image that is almost free of the zeroth-order term. Suppression of the DC term on the basis of the average-intensity method is similar to the application of a high-pass filter. The cutoff spatial frequency depends on the number of pixels used for calculating the average intensity of the selected pixels, see Fig. 1. When we select the larger number of pixels, the cutoff frequency increases. If we adopt a low cutoff frequency, the efficiency of the DC suppression is high, but there is significant loss of information in the reconstructed image. To prevent this loss while maintaining the DC suppression efficiency, we use a variable number of pixels. In conventional in-line digital holography, almost all low spatial frequencies are located close to the center of the hologram. Therefore, we use the various sizes of selected pixels for intensity averaging as a function of hologram location, as shown in Fig. 1. For example, we selected 30 pixels at the center of CCD (x ¼ 1024), while we selected 3 pixels at the outer CCD block (x ¼ 1 or 2048) as shown in Fig. 1.
3. Experimental setup and results Fig. 2 shows a schematic diagram of a transmission hologram microscope. The basic experimental setup is similar to that of a Mach—Zehnder-type interferometer. A 10 mW He–Ne laser is used as the light source and the objective lens of a microscope, ML, is used to expand the beam passing through the sample. We used neutral-density filters, VN, to obtain the maximum contrast of the interference patterns. A beam expander, BE, is used for the reference beam in the TEM00 mode. We used a CCD camera (Sony IPX4M15L) to record the holograms. The pixel size and the number of pixels are 7.4 mm 7.4 mm and 2048 2048, respectively. The CCD is located at a distance of 20 cm from the ML and the overlapping angle between the reference and objective rays is maintained at 01, thus leading to in-line holography. Fig. 3 shows (a) the hologram measured at a distance of 20 cm from the rear focal point of the objective lens, and (b) a
ARTICLE IN PRESS H. Cho et al. / Optics & Laser Technology 41 (2009) 741–745
Object M
ML
743
BS
O
CCD
R
VN
M
Laser BS
VN
BE
Fig. 2. Transmission-type digital holographic microscopy. VN: variable-density filter, BS: beam splitter, M: mirror, O: object wave, R: reference wave, BE: beam expander with spatial filter, ML: microscope objective lens.
Fig. 3. Hologram and reconstructed image with DC suppression: (a) hologram; (b) reconstructed image with twin-image elimination; (c) DC-suppressed image based on 3 3-pixel intensity averaging; and (d) DC-suppressed image based on intensity averaging using variable pixel numbers.
numerically reconstructed image at a distance of 75 cm from the CCD. The twin image is eliminated using the zero-padding method [11]. The Fresnel diffraction equation is used for numerical reconstruction of the images. As shown in Fig. 3(b), the bright central square region corresponds to the reconstructed zeroth-order diffraction image. Figs. 3(c) and (d) are the DC-suppressed images resulting from the ‘‘averaging’’ method. We used 3 3-pixel regions to calculate the average intensity in Fig. 3(c), and variable pixel numbers in Fig. 3(d). In Fig. 3(d) we used 10 10 pixels in the central part of the hologram, 7 7 pixels in the middle, and 3 3 pixels in the outer regions.
The DC-suppression ratio is defined as the ratio between the full intensity of the hologram and the intensity averaged over 80 80 pixels covering the central area of the reconstructed image. The DC-suppression ratios in Fig. 3(c) and (d) are similar, but the amount of information loss from the images is different. The image areas inside the dotted circles in Fig. 3(c) and (d) are different. From Fig. 3 we found that the DC-suppression ratios of the ‘‘average’’ and ‘‘variable-average’’ methods are similar, but the image quality is different. We could obtain better-quality images using the variable pixel number intensity-averaging method. Fig. 4 shows (a) a hologram, the grating pattern of which was measured at a distance of 20 cm from the rear focal point of the
ARTICLE IN PRESS 744
H. Cho et al. / Optics & Laser Technology 41 (2009) 741–745
Fig. 4. Hologram and DC-suppressed reconstructed images: (a) hologram; (b) DC-suppressed image after 3 3-pixel intensity averaging; and (c) DC-suppressed image using variable pixel number intensity averaging.
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Fig. 5. DC-suppression ratio and contrast: (a) DC-suppression ratio; (b) modulation transfer function; (c) gray level intensity of dotted line A in Figs. 4(b) and (c); and (d) gray level intensity of dotted line B in Figs. 4(b) and (c). The dotted and solid lines in panels (b) and (c) represent the results from the variable-pixel and the normal method, respectively.
objective lens, and (b, c) numerically reconstructed images at a distance of 75 cm from the CCD. Fig. 4(b) shows the DC-suppressed image using 3 3-pixel intensity averaging and Fig. 4(c) shows the DC-suppressed image using variable pixel numbers, as in Fig. 3(d). The images in Fig. 4(b) and (c) are different. We measured the gray level along the dotted lines in Fig. 4(b) and (c); the results are shown in Fig. 5(c) and (d).
Fig. 5(a) shows the DC-suppression ratio as a function of the number of pixels used for intensity averaging. Here, N(3) indicates that we used 3 3 pixels to calculate the average intensity, as suggested by Kreis and Juptner; A(3–10) indicates that we used 3 3 pixels in the outer regions of the hologram and 10 10 pixels in the central area to calculate the average intensity. Fig. 5(a) shows the DC-suppression ratio, which increases as the number of pixels used decreases. The suppression ratios from the method of
ARTICLE IN PRESS H. Cho et al. / Optics & Laser Technology 41 (2009) 741–745
Kreis and Juptner and the variable pixel number methods are similar. These results are reasonable as the averaging method is similar to the application of a high-pass filter. If we adopt a given cutoff frequency, higher frequencies are not influenced by the filter. Figs. 5(c) and (d) illustrate the measured gray levels along the dotted lines A and B in Fig. 4(b) and (c). From Fig. 5(c) and (d), it follows that the contrast of the gray level in the image reconstructed using the variable pixel number method is higher than that resulting from the ‘‘normal’’ (i.e., fixed number of pixels) averaging method. The contrast degrades rapidly in the central regions of the image based on the normal averaging method (solid lines in Fig. 5(c) and (d)). This degradation is caused by image information loss due to the averaging process. However, the variable pixel number averaging method does not degrade the image quality as much as the normal (fixed pixel number) averaging method. Fig. 5(b) shows the modulation transfer function (MTF) as a function of pixel number. The MTF also shows that we can obtain a higher quality DC-suppressed reconstructed image on the basis of the variable pixel number method.
4. Conclusions A simple method was developed to suppress the DC term in inline digital holographic microscopy images on the basis of the average intensity of variable instead of fixed numbers of pixels. The DC-suppression ratio is similar to that of the intensity-averaging method proposed by Kreis and Juptner, although the image quality in the new method is higher. As this new method is intrinsically simple and does not require any additional equipment, it is not sensitive to environmental disturbances and
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can also be used for dynamic measurements. This new method can thus significantly improve the quality of reconstructed images.
Acknowledgments This study was supported by the Korean Ministry of Commerce, Industry, and Energy. A number of the researchers participating in this study are supported by a grant from the ‘‘Second-phase BK21 project.’’ References [1] Cuche E, Marquet P, Depeursinge C. Simultaneous amplitude-contrast and quantitative phase- contrast microscopy by numerical reconstruction of Fresnel off-axis holograms. Appl Opt 1999;38:6994–7001. [2] Cuche E, Marquet P, Depeursinge C. Spatial filtering for zero-order and twin image elimination in digital off-axis holography. Appl Opt 2000;39:4070–5. [3] Xu L, Peng X, Guo Z, Miao J, Asundi A. Imaging analysis of digital holography. Opt Express 2005;13:2444. [4] Goodman JW. In: Introduction to Fourier optics. 2nd ed. New York: McGraw Hill; 2005. [5] Schnars U, Juepther W. In: Digital holography. Heidelberg: Springer; 2005. [6] Denis L, Corinne F, Thierry F, Christophe D. Twin-image noise reduction by phase retrieval in in-line digital holography. Proc SPIE 2005;5914:148. [7] Depeursinge C. In: Digital holography applied to microscopy. USA: Springer; 2006. [8] Takaki Y, Kawai H, Ohzu H. Hybrid holographic microscopy free of conjugate and zero-order images. Appl Opt 1999;38:4990–6. [9] Yamaguchi I, Zhang T. Phase-shifting digital holography. Opt Lett 1998;23:1221–3. [10] Kreis T, Juptner WPO. Suppression of the DC term in digital holography. Opt Eng 1997;36:2357–60. [11] Cho H, Kim D, Shin S, Jang W, Son J, Yu Y. Twin-image elimination in an in-line digital holographic microscope. J Korean Phys Soc 2008;52:1031–5.