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Digital holography is applied to measure the characteristics of transparent material. A digital hologram recording system to measure the surface of transparent material was established, and the digital holograms of transparent object were obtained in high quality. For postprocessing of hologram, the least-squares phase unwrapping algorithm was used in phase unwrapping, and the phase reconstruction image of transparent object was obtained. The information of material surfaces was measured and the characteristic was presented in 3D visualization. The validation experiment was conducted by NanoMap 500LS system; the results of validation experiment are well satisfied with the measurement by digital holography, which proved the feasibility of digital holographic technology as a good measurement tool for transparent material.

In 1948, Gabor [

Digital holography is a new image processing technology that uses a high-resolution charge-coupled device (CCD) camera for hologram recording and image reconstruction with a numerical method by a computer [

In general, the objects in applications of digital holography are not transparent, so the holograms were captured by the reflection of the object [

Noncontact surface measurement techniques are very important in many fields, such as science and engineering. It is very helpful to control the products quality and make the appropriate diagnosis. Digital holographic imaging as a new image processing technology, combined with optical holography and digital image processing of computer, is widely used in the field of surface measurements of objects. In addition to classical roughness values

Compared with other image processing and measuring techniques, digital holography has a number of important advantages [

Holographic interferometry (HI) is a procedure which enables static and dynamic displacements of objects with optically rough surfaces to be measured with optical interferometer accuracy [

Digital holographic recording optical path and the traditional optical holography are consistent; only replace holographic plate with a CCD camera as the recording medium. The concept of outline digital hologram recording is shown in Figure

Off-line recording of digital hologram.

The object wave

So the intensity distribution of the recorded hologram by CCD is written as

The light intensity is collected by the data acquisition card and quantity. The 3D information of object is saved by the computer and formed as a digital hologram.

In traditional holography, the reconstruction is carried out by means of illumination of the hologram intensity with the reference wave. A virtual image and a real image of the object are reconstructed. The digital hologram simulates the traditional optical reproduction processes, and its numerical reconstruction can be gained by computer.

The laser beam goes through the object and the part of the beam diffracted by objects and reaching the recording surface is considered the object beam, while the beam from the laser arriving without any distortion is considered as the reference beam. Two beams superposition create an interference pattern on the CCD sensor. This diffraction can be described by the Fresnel-Kirchhoff integral as [

The coordinates in (

Coordinate system for image reconstruction.

Different numerical reconstruction algorithms have been proposed, such as Fresnel approximation algorithm and convolution approach algorithm [

In this paper, we use numerical simulation hologram to check the ability of our arithmetic for determination of the focal plane. For numerical simulation reconstruction of holograms, the Fresnel and convolution arithmetic based on the reconstruction equations has been used well in practice. The convolution arithmetic producing good holograms and reconstruction images and high quality of holograms does not change with different object distances. Therefore, convolution arithmetic will be importantly explained in this paper.

In Figure

Because the form of (

As the material surfaces are uneven, when irradiated by the laser, there will appear a different phase on the material surfaces. In Section

Phase distribution value obtained by (

Phase unwrapping: (a) wrapped phase and (b) continuous phase.

Phase unwrapping is a technique which can generate a continuously phase distribution. It constitutes essential parts of optical metrology by heterodyne techniques. In surface measurement by digital holographic, the phase unwrapping is a key technique. Numerous phase unwrapping algorithms have been proposed in the past several years [

In this paper, the continuous phase image is acquired by least-squares phase unwrapping algorithm without weighing. The discrete cosine transforms (DCT) is used to solve the discrete Poisson equation in this method. The least-square solution of the unwrapped phase and the expanded phase is obtained.

As mentioned above, after the phase unwrapping with computer, the phase distribution

The surface of homogenous optical properties was measured in the light of the reconstructed phase-contrast image [

Since the height of the target surface is uniformly distributed, in this experiment a test target is used as the target surface. The optical experimental setup for recording test target (USFA 1950) holograms is shown in Figure

Experimental setup for recording test target holograms.

As shown in Figure

Figure

Data of heights.

Height | Min | Max | Average |
---|---|---|---|

Value (nm) | 72.7 | 79.1 | 78.8 |

Recording of digital hologram.

Reconstruction of digital hologram.

The reconstructed height distribution.

Height distribution.

The verification experimental equipment uses NanoMap 500LS which is produced by AEP technology, and the composition of the equipment is the same as the one in Figure

NanoMap 500LS.

Flow chart for taking a profile measurement.

After loading the test target onto the stage and setting up scan parameters, we can get the scan curve shown in Figure

Data of heights.

Height | Min | Max | Average |
---|---|---|---|

Value (nm) | 60.4 | 87.6 | 69.9 |

The scan curve.

The fitting curve.

Height distribution.

Tables

Comparison of the measurement results by two methods.

Methods | Digital holography (nm) | NanoMap 500Ls (nm) | Difference (nm) | Relative error (%) |
---|---|---|---|---|

Value | 78.8 | 69.9 | 8.9 | 12.7 |

In this paper, we have presented the digital holography for measuring the material surface as an important technique. The principle of surface measurement by digital holography is analyzed. In this paper, we use a target as a test target. By recording and reconstruction hologram, we obtain the phase and height distribution of the object surface by noise, phase unwrapping, and so forth. Then we use NanoMap 500LS 3D profilometer as validation experiment. Comprised of contact profilometer, the results of two measurement methods do not make much difference. However, digital holography measurement method has the larger advantage. Digital holographic measurement can obtain the surface of objects with no damage, high resolution, noncontact, and fast processing characteristics. And also, any measurement system has measuring error. Future research direction is to solve the measurement errors which exist.

This work was supported by the National Natural Science Foundation of China (11272368) and the Natural Science Foundation of CSTC (cstc2013yykfB0198).