Digital Holographic Encryption with Multiple-key Encoding using

Micro Phase-shifting Interferometry

Huang-Tian Chan

, Yang-Kun Chew

, Min-Tzung Shiu

and Chi-Ching Chang

Institute of Electro-Optical & Energy Engineering, Ming Dao University, Taiwan, ROC

School of Defense Science, National Defense University, Taiwan, ROC

Keywords: Digital Holography, Encryption, Phase-shifting Interferometry, Computer-Generated Hologram.

Abstract: This paper proposes a novel phase-shifting digital in-line holography with computer-generated holograms

(CGHs) to achieve the goal of encryption via multiple-key encoding. Multiple keys will also be required in

order to complete the decryption. These keys include the amplitude and the phase distribution of the primary

encryption key, the reconstruction distance of the image, and the phase value modulated via micro phase-

shifting interferometry. Experiments in this research have proved that the decryption would not be possible

without a primary key. The autocorrelation between the original and the decrypted images shows very high

similarity.

1 INTRODUCTION

Holographic encryption technology allows the

simultaneous encryption of both the phase and the

amplitude of 3-dimensional (3D) images. The

traditional holographic optical encryption allows

storing and fast accessing of high-density

information. Also, the complex encryption

conditions and restrictions make the encrypted

information hard to crack. This technology is an

important research area in the information

encryption. (Javidi 1994, Refregier 1995, Javidi

1997, Matoba 1999, Chang 2001, Sun 2002)

Denz et al. (

Denz 1991) has used deterministic

orthogonal phase codes in a reference-based

multiplexing technique to obtain a system for the

retrieval of multiple images with high diffraction

efficiency without energy losses, adjustment

problems, or time delay. However the system has

actual limitations that arise from imperfections in the

phase modulator. Among these limitations, spatial

phase fluctuations may destroy the orthogonality

between different phase addresses, which in turn,

causes cross-correlation noise.

Refregier and Javidi (Refregier 1995) have

proposed an optical encoding method of images for

security applications via random-phase encoding in

both the input and the Fourier planes. This method is

widely use in the field of optical encryption. One of

the simplest phase multiplexing techniques that have

been investigated by many researchers (

Wang 2000,

Chang 2002, Su 2004) is to use ground glasses to

perform random phase multiplexing. Random phase

encoding allows the information to be stored within

the recording medium in a more secured way.

However, the zero-order diffraction image and

the conjugate image interferences accompanied

traditional in-line holographic optical image

encryption technique tend to cause image distortion.

The strict reconstruction conditions of such

technique can also complicate the decryption and

sometimes cause information loss. Thanks to

charged coupled devices (CCDs) with suitable

numbers and sizes of pixels and computers with

sufficient speed, digital holography (DH) became

feasible.

Schnars and Jüptner (Schnars 1994) have

established the foundation of DH development using

a CCD as a holographic recording medium to

reconstruct a real image of an object from digitally

sampled hologram via numerical methods.

Accessing holographic information via CCD instead

of conventional recording media has been proved

feasible by many researchers (Liebling 2004,

Yamaguchi 1997, Zhang 1998, Javidi 2000,

Yamaguchi 2001). In the digital holographic

encryption, many researchers have been using object

beam or reference beam via phase mask or

wavefront modulation for encryption (Javidi 1996,

127

Chan H., Chew Y., Shiu M. and Chang C..

Digital Holographic Encryption with Multiple-key Encoding using Micro Phase-shifting Interferometry.

DOI: 10.5220/0004836601270133

In Proceedings of 2nd International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS-2014), pages 127-133

ISBN: 978-989-758-008-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

Javidi 2000, Tajahuerce 2000, Lai 2000, Arizaga

2003, Nishchal 2004, Naughton 2004, Carnicer 2005,

Meng 2006, Cheng 2008, Chen 2008, Zhang 2008,

Liang 2009, Jeon 2011). Kim et al. (Kim 2004) have

encrypted a digital hologram of a 3D object into a

stationary white noise using virtual optics, in which

a computer-generated random phase key is used.

Tsang et al. (Tsang 2011) have proposed a method

for fast numerical generation and encryption of a

Fresnel hologram. CCD does not work well when

the resolution of the interference fringes, due the

complexity of the encryption key, is beyond the

resolution limit of the CCD (Schnars 2002).

Therefore, this paper proposes to use in-line setup to

encrypt digital hologram. However, unavoidable

disturbance from zero-order diffraction image and

conjugate image will inevitably cause image

distortion.

Takaki et al. (Kreis 1997) have applied two

shutters and one phase modulator to the electro-

optical holographic recording system to change the

recording parameters for the elimination of zero-

order and conjugate images. Yamaguchi and Zhang

Yamaguchi 1997) have used piezoelectric transducer

to modulate the phase of the reference beam via

digital calculation, the double image interference of

the zero-order and conjugate images can be avoided

and phase information of the object beam obtained

(Zhang 1998). Cai et al. (Takaki 1999) have

proposed an approach to reconstruct the object wave

front in phase-shifting interferometry with arbitrary

unknown phase steps. The same research team Cai

2003) has proposed a method to extract the arbitrary

unknown and unequal phase steps in phase-shift

interferometry from interferograms recorded on the

diffraction field of an object. The object wave front

can then be digitally reconstructed with the formulas

they have derived. Throughout the years, researchers

have proposed similar techniques with different

formulas in a variety of experiments to suppress

double image interferences for the reconstruction of

object wave information Cai 2004, Xu 2008, Meng

2008, Chang 2009, Hsieh 2009, Hsieh 2010).

Another traditional digital technology like

encryption, decryption key information acquisition,

due to slight changes of environmental conditions

and CCD resolution and stability factors and the key

information in the different encryption, so will

certainly result in decrypt the information about the

error and loss. Implementation of the digital

holographic encryption and decryption work entirely

by numerical calculation, although we can to ensure

the invariance of the encryption key, but the biggest

drawback is the need to deal with complex 3D

images and phase information, as well as the

interference angle of diffraction transmission and

consideration of the 3D images with the polarization

direction and other issues, such as to achieve true

and a complete 3D image information, caused a

great deal of the burden must be on the operator and

time.

This paper uses micro phase-shifting (MPS)

digital in-line holography with CGHs for encryption

and decryption within the CCD resolution. The

comprehensive and low-noised holographic

information of the object wave and the encryption

keys are obtained after the elimination of the

conjugate and the zero-order diffraction images. The

decryption can be accomplished with CGHs as keys

without losses. Based on this hybrid approach, the

information that has been encrypted can only be

correctly obtained by not only the correct multiple

keys but also correct parameters. Therefore, it

demonstrates that this approach can be used enhance

the feasible performance of digital holographic

encryption.

2 WORKING PRINCIPLE

The experiment is conducted using Mach-Zehnder

interference setup as shown in Fig. 1. The light

source of this setup is a He-Ne laser with a power of

30 mW and a wavelength of 632.8 nm. The setup

adopts two λ/2 wave-plates and a polarized beam

splitter (PBS) to adjust the ratio of the object beam

and the reference beam. Both beams are collimated

as plane waves via a lens and a spatial filter. The

phase object is a 1.77 mm glass plate (refractive

index = 1.52) placed in the path of the reference

wave. The plate can be rotated to micro adjust the

phase of the reference beam and thereby modify the

optical path of the beam. The hologram is recorded

using a CCD sensor (Pixera-150SS CCD camera,

1392×1040 pixels, 6.5 mm by 4.84 mm). The CCD

acquires and stores the digital image of the

interferences of the reference beam and the object

beam. The object beam is thereby reconstructed

while the beam’s phase change can be obtained via

calculation.

This research starts with traditional digital

holographic optical encryption methods for the

encryption and decryption testing. And then

improves the procedure with the optical capture

image along with the computer-generated hologram

encryption for simple and high security encryption.

Using reference beam modulated by arbitrary

phase or amplitude device

(, )Txy

and conducting

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Figure 1: Experiment setup of AMPS modulated digital

holographic microscopy encryption.

Fresnel diffraction at distance d in free space, the

phase modulated reference beam ψ

key

can be

obtained via Eq. (1) (Goodman 2005):













-1

key

(,)= = ( )Th T hzd





  

(1)

Then interfere the coaxial structure and the

object beam on the recording plane,









, to

speedily and securely encrypt the information of the

beam with hologram,

1enc

, via equation (2):

22 2* *

1 key key key key

||||||

enc O O O O



 

   

(2)

The input image of this experiment is shown in

Fig. 2(a). The encrypted image obtained when the

distance from CCD to the input image is 21.5 cm

and to the lenticular lens array (LLA) is 7.6 cm is

shown in Fig. 2(b).

(a) (b)

Figure 2: (a) Input mage and (b) image with LLA

encryption.

The first step of the holographic information

decryption is zero order term suppression:

'22**

11key key key

||||

enc enc O O O





   

(3)

This is the first decryption key. The reduced

intensity of the hologram after complete suppression

of the zero order term is:

'22

key key

+exp()||||

exp(- ) exp( )

enc O O

   

  





(4)

Where





can be any value other than





can any integer) (Zhang, 2004).

This is the second decryption key. To suppress the

conjugate image, multiply Eq. (5) with









jexp

then subtract it from Eq. (4) to obtain:





'' *

12 key

-exp(- ) = 1-exp(- 2 )

enc enc O

IiI i







(5)

When





is 1.30 rad, the image and the phase

contrast image of primary key (LLA) after traveling

7.6 cm in the free space are shown in Figs 3(a) and

3(b).

(a) (b)

Figure 3: (a) Image of primary key (LLA) and (b) phase

contrast image of primary key.

As per Eq. (5),

key



, the conjugate information

of the primary key needs to be removed in order to

obtaind the complete information of the original

object beam, This process is the fourth decryption

key, which is the most difficult to obtain. As shown

in Fig 4(a), It is impossible to complete decrypt the

image without this key even if all other keys are

compromised. Fig. 4(b) shows the complete image

decrypted with this primary key.

(a) (b)

Figure 4: (a) Decrypted image before applying primary

key and (b) image after complete decryption.

The last decryption key is the distance between

the encrypted image and the CCD (

d), which is used

for final decryption.

The object beam as well the image and the phase

of the key obtained via experiment are shown in Figs

5(a), 5(b), 3(a), and 3(b). The digital holographic

encryption as shown in Fig 5(C) can then be

achieved via computer generated hologram

production technique.

The image decrypted with all the required

decryption keys is shown in Fig. 6(a). The cross-

correlation of the decrypted image and the original

input image is shown in Fig. 6(b). The similarity of

DigitalHolographicEncryptionwithMultiple-keyEncodingusingMicroPhase-shiftingInterferometry

129

(a) (b) (c)

Figure 5: Comparison of (a) image (not encrypted) at 21.5

cm from CCD, (b) phase comparison image, and (c) image

after holographic encryption.

these two images is close to 100%, compared to the

result of 85% similarity, as shown in Fig. 6(c), via

traditional decryption technique. This result

indicates that the proposed encryption technique can

provide effective and highly secured digital

holographic encryption without distortion.

(a) (b) (c)

Figure 6: (a) Image after complete decryption (b) cross-

correlation of the input image and Fig. 7(a)., and (c) cross-

correlation of the input image and Fig. 5(b).

3 RESULTS AND DISCUSSION

The experiment is conducted using Mach-Zehnder

interference setup slightly different from the one

shown in Fig. 1. In this setup, a plane wave is used

as the recording reference beam. With the position

of CCD unchanged, the object beam as well as the

image and phase information of all the primary keys

are acquired individually.

The system resolution tests have been performed

using a Newport resolution target (RES-1) as an

object. The original input image acquired by the

CCD is shown in Fig. 7(a). The image acquired at a

9.4 cm distance between the CCD and the resolution

target and the phase comparison image are shown in

Figures 7(b) and 7(c), respectively.

(a) (b) (c)

Figure 7: Comparison of (a) original input image, (b)

image at 9.35 cm from CCD, and (c) phase comparison

image of (a) and (b).

Use computer-generated hologram to encrypt the

target image (Fig. 8(a)). For the purpose of

decryption testing, the numerical summation of Figs

3(a) and 7(b) are used to produce encrypted image of

no interference (Fig. 8(b)). Apply Eq. (5) at





to produce another encrypted hologram of

modulated reference beam phase (Fig. 8(c)).

(a) (b) (c)

Figure 8: The encryption images of analytical target. (a)

holographic encryption image without phase modulation,

(b) encryption image without interference, and (c)

holographic encryption image with phase modulation.

The sensitivity analysis of key rotation and key

shifting tests are conducted to verify the integrity of

the proposed technique. To produce the adjusted

images for analysis, the key image is digitally

rotated and shifted. The obtained images are then

decrypted with the accordingly adjusted keys. The

tolerance of rotation and shifting are then examined

through the cross correlation between these

decrypted images and the image treated via ordinary

procedure. Figure 9 shows that the similarity is

below 30% when the decryption key is rotated over

0.4

degree. Figure 10 shows that the image becomes

not decryptable when the decryption key is shifted

over two pixels (9.34 μm).

Figure 9: Sensitivity analysis of key rotation at decryption.

Figure 10: Sensitivity analysis of key shifting at

decryption.

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The image of Lena as shown in Fig. 11(a), which is

commonly used for image analysis and processing,

is used in this research to verify the researched

technique’s influence to the encrypted image. In

addition, a numerical equation is used to simulate

the condition in which the distance between CCD

and the Lena image is 10.0 cm. The result of the

simulation and the obtained relative phase-contrast

image and the phase information are shown in Fig.

11(b) and Fig. 11(c).

(a) (b) (c)

Figure 11: (a) Original input image, (b) image at 10 cm

from CCD, and (c) phase comparison image of (a) and (b).

Multiple digital holographic encryptions are

performed using LLA and the primary key

(diffuser), the image and the phase information

obtained as contrast to the CCD are shown in Figs

3(a), 3(b), 12(a), and 12(b).

(a) (b)

Figure 12: (a) Image of primary key (diffuser) and (b)

phase comparison image of primary key.

The hologram encrypted with these two primary

keys is shown in Fig. 13(a). This multi-digital

holographic encryption is able to process and

achieve the encryption effect that is difficult for the

conventional optical hologram encryption technique.

Figure 13(b) shows the image decrypted with a

reconstruction distance of 10.0 cm.

(a) (b)

Figure 13: (a) Encrypted image after multiple digital

encryption and (b) decrypted image when reconstruction

distance (d = 10.0 cm) is the only known key.

The decryption test of the second key set is

conducted using zero-order term elimination

technique. The result is shown in Fig. 14(b). The test

of the third key set is conducted via conjugate term

elimination with the result shown in Fig. 14(a). Even

if all other key sets including the primary key (LLA)

are cracked, it is still impossible to obtain complete

image information without another primary key (the

diffuser).

(a) (b) (c)

Figure 14: Resulted image (a) after applying two sets of

decryption keys, (b) after applying three sets of decryption

keys, and (c) before applying primary key (diffuser).

The image decrypted with all the required

decryption keys is shown in Fig. 15 (a). The result of

the cross-correlation operation

of the decrypted

image and the original input image is shown in Fig.

15 (b). The similarity of these two images is close to

100%, which indicates that the proposed encryption

technique can provide effective and highly secured

digital holographic encryption without distortion.

(a) (b)

Figure 15: (a) Image after complete decryption; (b) related

operation result of input image and Fig. 14 (a).

4 CONCLUSIONS

This research uses optical interferometry and digital

image processing technique to capture, via in-line

setup and within the CCD resolution limit, the

holographic information of the object beam and the

encryption key. The encryption can be completed

using the computer generated holograms with

multiple keys that include 1) the amplitude and the

phase distribution of the primary encryption key, 2)

the reconstruction distance of the image, 3) the

elimination of zero-order term, and 4) the phase

value modulated via arbitrary micro phase-shift

interferometry.

This study has shown that the decryption is not

achievable without a primary key. The encrypted

DigitalHolographicEncryptionwithMultiple-keyEncodingusingMicroPhase-shiftingInterferometry

131

image can be transmitted to and captured by a CCD

at the receiving end, and then decrypted via simple

logical operations. The autocorrelation between the

original and the decrypted images shows 100%

similarity. The decrypted 3D image can be displayed

via the holographic display technology. Having the

integrity that is comparable to that of traditional

optical holographic encryption, this technique has

the convenience and simplicity of digital

holographic processing and thus provides a secured

solution for holographic information transmission.

ACKNOWLEDGEMENTS

The authors would like to thank the National Science

Council of the Republic of China, Taiwan, for

financially supporting this research under Contract

No. NSC 102-2221-E-451-019.

REFERENCES

Javidi, B., Horner, J. L., 1994. Optical pattern recognition

for validation and security verification .Opt. Eng. 33

(6): pp. 1752-1756.

Refregier, P., Javidi, B., 1995. Optical image encryption

based on input plane and Fourier plane random

encoding. Opt. Lett. 20(7): pp. 767-769.

Javidi, B., Zhang, G., Li, J., 1997. Encrypted optical

memory using double-random phase encoding. Appl.

Opt. 36(5): pp.1054-1058.

Matoba, O. and Javidi, B., 1999. Encrypted optical

storage with wavelength-key and random phase codes.

Appl. Opt. 38(32): pp. 6785-6790.

Chang, C. C., Russell, K. L., Hu, G. W., 2001. Optical

holographic memory using angular-rotationally

phase-coded multiplexing in a LiNbO

:Fe crystal.

Appl. Phys. B. 72(3): pp. 307-310.

Sun, C. C., Su, W. C., 2002. Three-dimensional shifting

selectivity of random phase encoding in volume

holograms. Appl. Opt. 40 (8):pp. 1253-1260.

Denz, C., Pauliat, G., Roosen, G., 1991. Volume hologram

multiplexing using a deterministic phase encoding

method. Opt. Commun. 85(2-3): pp. 171-176.

Wang, B., Sun, C. C., Su, W. C., Chiou, A. E. T., 2000.

Shift-tolerance property of an optical double-random

phase-encoding encryption system. Appl. Opt. 39 (26):

pp. 4788-4793.

Chang, H. T., Lu, W. C., Kuo, C. J., 2002. Multiple-phase

retrieval for optical security systems by use of

random-phase encoding. Appl. Opt. 41(23): pp. 4825-

4834.

Su, W. C., Sun, C. C., Chen, Y. C., Ouyang, Y., 2004.

Duplication of phase key for random-phase-encrypted

volume holograms. Appl. Opt. 43(8): pp. 1728-1733.

Schnars, U., Jüptner, W., 1994. Direct recording of

holograms by a CCD target and numerical

reconstruction. Appl. Opt., 33 (2): pp. 179-181.

Liebling, M., Blu, T., Unser, M., 2004 .Complex-wave

retrieval from a single off-axis hologram. J. Opt. Soc.

Am. A. 21(3): pp. 367-377.

Yamaguchi, I., Zhang, T., 1997. Phase-shifting digital

holography. Opt. Lett. 22(16): pp. 1268-1270.

Zhang, T., Yamaguchi, I., 1998. Three-dimensional

microscopy with phase-shifting digital holography.

Opt. Lett. 23(15): pp. 1221-1223.

Javidi, B., Tajahuerce, E., 2000. Three-dimensional object

recognition by use of digital holography. Opt. Lett.

25(9): pp. 610-612.

Yamaguchi, I., Kato, J., Ohta, S., Mizuno, J., 2001. Image

formation in phase-shifting digital holography and

applications to microscopy. Appl. Opt. 40(34): pp.

6177-6186.

Yamaguchi, I., Ohta, S., Kato, J., 2001. Surface

contouring by phase-shifting digital holography. Opt.

& Lasr. Tech. 36(5):pp. 417-428.

Javidi, B., Zhang, G., Li, J., 1996. Experimental

demonstration of the random phase encoding

technique for image encryption and security

verification. Opt. Eng. 35 (9): pp. 2506-2512.

Javidi, B., Nomura, T., 2000. Securing information by use

of digital holography. Opt. Lett. 25(1): pp. 28-30.

Tajahuerce, E., Matoba, O., Verrall,S. C., Javidi, B.,2000.

Optoelectronic information encryption with phase-

shifting interferometry. Appl. Opt. 39(14): pp. 2313-

2320.

Tajahuerce, E., Javidi, B., 2000. Encrypting three-

dimensional information with digital holography.

Appl. Opt. 39(35): pp. 6595-6601.

Lai, S., Neifeld, M. A., 2000. Digital wavefront

reconstruction and its application to image encryption.

Opt. Commun. 178(4-6): pp. 283-289.

Arizaga, R., Henao, R., Torroba, R., 2003. Fully digital

encryption technique. Opt. Commun. 221(1-3) pp. 43-

47.

Nishchal, N. K., Joseph, J., Singh, K., 2004. Fully phase

encryption using digital holography. Opt. Eng. 43(12):

pp. 2959-2966.

Naughton, T. J., Javidi, B., 2004.

Compression of

encrypted three-dimensional objects using digital

holography. Opt. Eng. 43(10): pp. 2233-2238.

Carnicer, A., Montes-Usategui, M., Arcos, S., Juvells, I.,

2005. Vulnerability to chosen-cyphertext attacks of

optical encryption schemes based on double random

phase keys. Opt. Lett. 30(13): pp. 1644-1646.

Meng, X. F., Cai, L. Z., Xu, X. F., Yang, X. L., Shen, X.

X., Dong, G. Y., Wang, Y. R., 2006. Two-step phase-

shifting interferometry and its application in image

encryption. Opt. Lett. 31(10): pp. 1414-1416.

Cheng, X. C., Cai, L. Z., Wang, Y. R., Meng, X. F.,

Zhang, H., Xu, X. F., Shen, X. X., Dong, G. Y., 2008.

Security enhancement of double-random phase

encryption by amplitude modulation. Opt. Lett. 33(14):

pp. 1575-1577.

PHOTOPTICS2014-InternationalConferenceonPhotonics,OpticsandLaserTechnology

132

Chen, G. L., Yang, W. K., Wang, J. C., Chang, C. C.,

2008. Deterministic Phase Encoding Encryption in

Single Shot Digital Holography. Appl. Phys. B. 93(2-

3): pp. 473-479.

Zhang, Y., Wang, B., 2008. Optical image encryption

based on interference. 2008. Opt. Lett. 33(21): pp.

2443-2445.

Xiao, Y.L., Zhou, X., Wang, Q.H., Yuan S., Chen, Y.Y.,

2009. Optical image encryption topology. Opt. Lett.

34(20): pp. 3223-3225.

Jeon, S. H., Gil, S. K., 2011. 2-step Phase-shifting Digital

Holographic Optical Encryption and Error Analysis.

Journal of the Optical Society of Korea. 15(3): pp.

244-251.

Kim, H., Kim, D. H., Lee, Y. H., 2004. Encryption of

digital hologram of 3-D object by virtual optics. Opt.

Express. 12(20): pp. 4912-4921.

Tsang, P. W. M., Poon, T. C., Cheung, K. W. K., 2011.

Fast numerical generation and encryption of

computer-generated Fresnel holograms. Appl. Opt.

50(7): pp. B46-B52.

Schnars, U., Juptner, W., 2002. Digital recording and

numerical reconstruction of holograms. Measurement

Science and Technology. 13(9): pp. R85- R101.

Kreis, T., Juptner, W., 1997. Suppression of the dc term in

digital holography. Opt. Eng. 36(8):pp. 2357-2360.

Takaki, Y., Kawai, H., Ohzu, H., 1999. Hybrid

holographic microscopy free of conjugate and zero-

order images. Appl. Opt. 38(23): pp. 4990-4996.

Cai, L. Z., Liu, Q., Yang, X. L., 2003. Phase-shift

extraction and wave-front reconstruction in phase-

shifting interferometry with arbitrary phase steps. Opt.

Lett. 28(19): pp. 1808-1810.

Cai, L. Z., Liu, Q., and Yang, X. L., 2004. Generalized

phase-shifting interferometry with arbitrary unknown

phase steps for diffraction objects. Opt. Lett. 29(2):

pp. 183-185.

Xu, X. F., Cai, L. Z., Wang, Y. R., Meng, X. F., Sun, W.

J. , Zhang, H., Cheng, X. C., Dong, G. Y., Shen, X. X.,

2008. Simple direct extraction of unknown phase shift

and wavefront reconstruction in generalized phase-

shifting interferometry: algorithm and experiments.

Opt. Lett. 33(8): pp. 776-778.

Meng, X. F. , Cai, L. Z. , Wang, Y. R. , Yang, X. L., Xu,

X. F., Dong, G. Y., Shen, X. X., Cheng, X. C., 2008.

Wavefront reconstruction by two-step generalized

phase-shifting interferometry. Opt. Commun. 281(23):

pp. 5701-5705.

Chang, C. C., Hsieh, W. T., Kuo, M. K., 2009. Digital

Holography with arbitrary phase-step reconstruction

using multiple holograms. Proc. SPIE, 7358: pp.

735813-1-735813-11.

Hsieh, W. T., Kuo, M. K. , Yau, H. F., Chang, C. C. 2009.

A simple arbitrary phase- step digital holography

reconstruction approach without blurring using two

holograms. Opt. Rev. 16(4):pp. 466-471.

Hsieh, W. T., Kuo, M. K., Chang, C. C., 2010. Wavefront

reconstruction with fresnel holograms by arbitrary

phase-Step digital Holography. Journal of C. C. I. T.

39(1): pp. 229-238.

Goodman, J. W., 2005. Fourier Optics, Roberts &

Company. Colorado, 3rd ed.

Zhang, Y., Pedrini, Osten, G., W., Tiziani, H. J., 2004.

Reconstruction of in-line digital holography from two

intensity measurements. Opt. Lett. 29(15): pp.1787-

1789.

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