There are many ways. For example, before angular spectrum you should take fourier filtration to eliminate zero  and -1 orders images.

That is the problem. I can not ensure whether the object is in focus because of  the depth of focus. So I can not get a perfect hologram. Could you give me some advice? Thank you very much.

If focus is the problem, consider that if you cannot distinguish the difference it is very likely because there is no difference. Depth of focus gives you room for error.

Anyway you could use a criterion, see, for instance: 

http://www.opticsinfobase.org/oe/fulltext.cfm?uri=oe-14-13-5895&id=905424

If it is other type of problems, take into account that angular spectrum is valid only for short distance, for long ditsance you'd rather use a convolution method. You could take a look to the Kreis book or to this reference:

http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-45-6-1102

Dear professor Garcia-monreal

      Thank you very much.  I think I have learned much from them. However, my another question about the phase unwrapping also needs to be answered. Could you give me a hand? Hope to hear from you soon.

The reconstructed image quality also depends on the principles of the digital hologram construction. I recommend using the methods of so called focusators and deep kinofoms. Look:

Victor A. Soifer. Methods for Computer Design of Diffractive Optical Elements. John Wiley & Sons, Inc.New York, NY, USA©2001 ISBN:0471095338

References [20-27] related to multiorder diffractive lenses and deep kinoforms in https://www.researchgate.net/publication/6726807_Achromatic_optical_elements

Article Achromatic optical elements

Dear Mingqing Wang,

From your question I could understand that you are using plane waves. But more information is needed to answer your question. Is your hologram in-line or off-axis? Is it in-line or Gabor in-line? What are the parameters, such as wavelength, distances, object size?  Thank you in advance!

Kind regards,

Tatiana

Dear Tatiana Latychevskaia

Yes, you are right. I am using plane waves.My hologram is off-axis, wavelength is 671 nm, and the distance is decide by the lense, the length of object  is 1.5 centimeter and the width is 1 centimeter. Could you give me some advice? Thank you in advance!

You could share your hologram  so I can try to reconstruct it. 

Dear Mingqing Wang,

thank you for your answer, can you provide a sketch of your setup or a reference to an article with similar setup? Thank you!

The two pictures could answer your two questions. Thank you!

Thank you, Mingquing, for uploading the two images.

I think the problem is the quality of the hologram, it is very noisy and the interference pattern is buried under the noise. In the left top corner you have a small object, whose hologram looks about right to be reconstructed by ASM. But, I think you are interested in the large object in the center, whose hologram does not exhibit any fringe pattern (or is just problem of bmp format?). I would suggest you to get a better signal-to-noise ratio hologram and improve the visibility of (1) interference pattern given by superposition with the reference wave, and (2) interference pattern given by the object wave alone. You can check that under Fourier transform of an off-axis hologram, one should see two sidebands for +1 and -1 orders. At the moment, Fourier transform of your hologram gives only two faint spots at the currying frequencies.

Two questions before going further :

- it looks like if the object is diffusive. Is it right?

- I understand that the object is imaged to infinity so that a point in the object makes a plane beam in the sensor. Otherwise the divergence of the beams (reference and object) in the sensor would be very different, resulting in very high frequencies in the hologram. This would limit a lot the resolution.

Dear Tatiana Latychevskaia 

Thank you very much!  My  hologram does not exhibit any fringe pattern? But the hologram is diffusive in the area of Chinese character. As far as I am concerned, that is the fringe pattern. Am I wrong? 

Dear professor Garcia-Monreal

The object is a clear Chinese character. As far as I am concerned，the object is diffuse because of the exsistance of fringe pattern. At the same time, I agree that there are  very high frequencies in the hologram. But  I have no ideas to remove them. Could you give me some ideas? By the way ,may I have an example of image plane digital hologram of your group? Thank you so much for all the help that you have been giving me.

I still do not see clear the situation. The object looks difussive. I just made a test lensless Gabor hologram (I did it on my desk, sorry for the noise in the beam coming form the laser pointer). With a pixel spacing of 10e-3 mm and lambda of 0.5e-3 mm you can focus it at 228 mm. (not true distance, because illumination was not collimated). You can see noise from the illumination but not a speckle pattern, that is usually due to diffussive object.

The hologram itself has fringes arround the shadow of the larges objects.

Exact image plane hologram can sometimes be a bad choice, because it will need a high intensity reference and image divergence is high. Try defocusing before recording. 

Also try that the divergence of all beams involved (illumination, object divergence and reference be as close as possible, to minimize spatial frequenncies.

Dear professor Garcia-Monreal

Thank you very much for uploading your hologram. However I do not know what is the shape of the object. Could you give me a picture of the object for comparison？Tomorrow is Christmas Day. Wish you a merry Christmas and a happy new year.

the object is an USAF 1951 resolution target. Try to propagate and soon you will see the large blocks. small ones need a fine focussing.

As far at it applies in China, merry Xmas and the best for 2015!