0 Preface
As an important tool for 3D reconstruction of objects and measurement of topography, digital holography [1] has broad application prospects in object measurement such as microcircuit detection, particle size detection and transparent field measurement [2-5]. Digital holography is usually recorded with a coherent light source (laser), and its good coherence makes the experiment very simple. However, fully coherent light can be very sensitive to any small defects in the optical path, and strong coherence can also cause speckle noise and high frequency fringe noise due to multiple reflections in the component, which can affect holography. The quality of the graph has an extremely adverse effect and also leads to a reduction in the quality of the reconstructed wavefront. Many methods, such as the Rotating Diffuse method and the digital image processing method [6], have been proposed to attenuate and eliminate these noises, but these methods have their own limitations, often relying on specific experimental devices and specific objects. . In recent years, some coherent optical holography techniques have gradually gained attention [7]. Due to the low temporal coherence and spatial coherence of partially coherent light, some of the above noises are greatly weakened or even eliminated, thus significantly improving holography. Figure and reconstruct the quality of the light wave field. In this paper, ordinary commercial high-brightness light-emitting diodes (LEDs) are used for digital holographic research. Compared with laser light sources, LEDs are small in size and low in price, and do not require special driving devices. The experimental results confirm the practicability of this kind of LED in digital holography, and the quality of the partially coherent optical digital hologram based on LED and the quality of light field reconstruction are greatly improved compared with the use of laser light source.
1 Experimental device and light source coherence study
1. 1 experimental device
The experimental device is shown in Figure 1. After the light from the light source is concentrated by the lens L1, it is first filtered by the pinhole PH, then collimated by the lens L2, and enters the modified Michelson interferometer. At this time, the incident light is splitter mirror (BS). ) Divided into 2 beams, one beam is reflected by the plane mirror M to generate plane reference light waves. The plane mirror M is attached to a piezoelectric ceramic micro-displacer (PZT) for phase shifting the reference light. Another part of the incident light illuminates the object to be measured (OBJ) to generate the object light wave, and the object light wave and the reference light wave are recombined by the beam splitter and then reach the CCD surface, and the formed interference pattern is recorded by the CCD.
Figure 1 LED digital holographic experimental device based on LED
1. 2 The specificity of LED light source and experimental measures
The LED used in the experiment is a common commercial red LED with a light-emitting surface diameter of 2. 5 mm and a maximum power consumption of 3 W. In general, such LEDs are not used in digital holography. Therefore, its basic parameters must be studied, including spectral distribution and temporal and spatial coherence.
1. 2. 1 LED time coherence
In the Michelson interferometer, the optical path difference of the two beams of light obtained after the splitting of the incident light is d, and for the quasi-single light, the interference fringe from the clearest to the disappearance is defined as the coherence length Lc. Lc can be expressed by the following formula [8]:
Where: K is the central wavelength of quasi-monochromatic light; ΔK is the half-peak spectral line width of quasi-monochromatic light. To determine the coherence length of the LEDs used, we used a spectrometer to determine the spectral distribution of the LEDs used in the experiment, as shown in Figure 2.
Figure 2 Normalized LED spectral distribution
8微米。 The center wavelength λ ≈ 655 nm, the half-peak line width λ △ = 24 nm, so its coherence length Lc = λ2 / λ △ ≈ 17. 8μm. It can be seen that the coherence length is very small, and the corresponding interference fringes only exist in a space of more than ten micrometers. Therefore, when applying LED for digital holography, it is first necessary to use laser to calibrate, that is, first use laser as the light source, adjust the optical path difference of the two beams to be close to each other, and then use LED instead of laser light source for fine adjustment until clear interference occurs. stripe. Figure 3 shows the interference fringes of the LEDs taken with the gradual increase in the optical path difference of the two beams on the Michelson interferometer. Obviously, beyond the coherence length of the LED, the interference fringes will disappear. Of course, to change the coherence length of the LED, it is necessary to change its spectral distribution, which is very difficult to do. It can be seen that one limitation of LEDs applied to digital holography is that the fluctuation of the object itself cannot exceed the coherence length of the LED, otherwise holographic interference cannot be performed. Therefore, in the digital holography based on LED, the thickness of the measured object should be Micron or nanoscale.
1. 2. 2LED spatial coherence
When using optical diffraction theory and digital holography theory for analysis and calculation, the light source is generally considered to be completely coherent light.
LED as a typical partially coherent light source, strictly speaking, cannot be calculated using the theory of coherent imaging, it can only be applied to partial coherence theory. However, statistical optics theory states that, under certain conditions, the entire system can behave like a fully coherent system despite partial coherent light illumination. This condition is: Partially coherent light sources are so small that the coherence area produced on the object significantly exceeds the area of ​​the imaging system's amplitude spread function [9]. Under such requirements, in general, LED light sources must be pinhole filtered to achieve sufficiently high spatial coherence. Figure 4 shows the diffraction image (diffraction distance Z = 15 cm) of the object (USAF 1951 resolution plate) in the two cases without pinholes and pinholes in the device shown in Figure 1.
Figure 3 Interference fringes of the LED on the Michelson interferometer (from (a) to (d) the optical path difference of the two arms increases in turn)
Figure 4 Diffraction image of the USAF-1591 resolution plate
It can be seen from Fig. 4 that the diffraction image of the object without the pinhole is very blurred, and the diffraction image becomes clear after the pinhole is added, that is, the diffraction of the object transitions from the partially coherent diffraction to the nearly complete coherent diffraction. In general, the smaller the pinhole diameter, the better the coherence is obtained. However, if the pinhole is too small, the incident light intensity is too weak, which makes recording difficult, and accordingly, the power of the LED must be increased. Therefore, we chose pinholes with φ=100 Lm and high-brightness LEDs with a maximum power of 3 W for experiments. In fact, the pinhole-filtered light source still cannot obtain particularly high coherence, and the interference fringes can be observed in a very small range of the angle θ between the reference light and the object light. For off-axis digital holography, in order to achieve the separation of the spectral components of the holographic surface, [10]:
Where: Z represents the holographic recording distance; LxCCD and Lxobj represent the linearity of the CCD and the recorded object in the x direction, respectively. Experiments have shown that θ cannot satisfy equation (2) in the range where interference fringes can be observed. Therefore, LED-based digital holography can only be limited to the range of coaxial holography, that is, digital holography can only be performed by the phase shift method. This is why we use Figure 1 as the holographic device.
2 Principle of phase shift digital holography
When the four-step phase shift is performed using the apparatus shown in Figure 1, the intensity Ii(x,y) recorded by the four CCDs is
Where: Io(x,y) and Ir(x, y) are the intensity distributions of the object light wave and the reference light wave on the CCD surface, respectively; the relative phase distribution of the object light wave and the reference light wave on the CCD surface; φ= (i - 1) π/2 is the phase shift produced by the piezo mirror driven mirror. The complex amplitude distribution Od(x, y) of the object light wave on the CCD surface can be given by:
When determining the holographic recording distance, the recording distance is limited by the following formula [10]:
Where: Z represents the holographic recording distance; LxCCD and Lxobj represent the linearity of the CCD and the recorded object in the x direction, respectively; Δx represents the pixel size of the CCD in the x direction. Obviously, under the condition that the formula (5) can be satisfied, the holographic recording distance should be shortened as much as possible, so as to record as many frequency components as possible to obtain better image quality. Therefore, it is very likely that the recording distance does not satisfy the Fresnel approximation condition, so the original object light wave should be reconstructed by the angular spectrum method. The transfer function of the system in the frequency domain during inverse diffraction is
Where: fx, fy is the spatial frequency; Z is the distance from the object to the CCD; λ is the recording wavelength. The reconstructed light wave complex amplitude can be expressed as
Where F and F-1 represent the Fourier transform and the inverse Fourier transform, respectively. Therefore, the strength and phase of the measured object can be expressed as
