Only a beam of laser light will not spread and diffuse. In lasers, waves are identical and in phase, which produces a beam of coherent light. There are many types of lasers that use gases such as helium, neon, argon, and carbon dioxide. Lasers also use semiconductors Galiodium and Arsenic , solid-state material ruby, glass , and even chemicals hydrofluoric acid in their operation.
With the cavity of the laser the beam of light is reflected back and forth along the central tube, until the waves of light become coherent. Movement of light in a laser. In fact, the word "laser" is actually an acronym that stands for "Light Amplification by Stimulated Emission of Radiation" 1.
What is coherence? In the simplest picture, you can visualize a beam of light as a bundle of many little sine waves traveling through space. In this picture, coherence means that all the respective peaks of the various sine waves are lined up in space, and continue to stay lined up as the waves travel. By the phrase "lined up", we mean that if you were able to take a snapshot at a certain time of the different wave components in a light beam, you would find that all the first peaks are at the same location in space, all the second peaks are at the same distance, etc.
In order for the peaks to stay completely aligned everywhere, a few things have to happen:. The waves have to have approximately the same wavelength temporal coherence If one wave has its consecutive peaks separated by a distance of nanometers, and another wave has its peaks separated by a distance of nanometers, then it should be obvious that if you line up one pair of peaks, you cannot line up any of the other pairs of peaks.
Ideally, if all the wave components had exactly the same wavelength and the other criteria listed below were met , then all the peaks could be lined up perfectly, forever. Such a situation is actually physically impossible. It would take an infinitely long beam of light in order to have all the wave components have exactly the same wavelength the proof of this statement is not obvious and requires Fourier analysis.
Despite the fact that an exactly single-wavelength beam of light is physically impossible, we can get very, very close. In fact, having a light beam that is very close to single-wavelength called "monochromatic" is one of the main reason lasers are so useful.
Using monochromatic light can allow us to measure or trigger a very specific response in a material e. The waves have to be in phase spectral coherence The phase of a wave describes what part of a sine wave's cycle exists at a certain reference point.
Therefore, even if two waves have the same wavelength, if one wave is shifted forward a bit relative to the other wave, their peaks will not be aligned. The phase of the various waves in a beam must be the same in order for their peaks to be aligned and for the beam to be spectrally coherent.
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Camy, J. Bengoechea, U. Fechner, F. Reichert, N. Hansen, K. Varsanyi: Surface lasers, Appl. Meanwhile, the experimental spatial coherence values are in good agreement with the theoretical ones, and both of them are not monotone decreasing when we increase the emitting size of the light source. Besides, the interference fringes is regarded as sharp when the pinhole size is smaller than 0.
Therefore, we consider it as feasible to use LEDs in digital holographic displays to achieve sharp reconstructed images, if the size of its emitting area is smaller than 0. Apart from limiting the emitting size of an LED, we can also increase its spatial coherence by increasing the distance of its light propagation.
For a uniform light source propagating in free space, we can calculate the theoretical spatial coherence values shown in Eq. For the experimental measurements, we use the same double slits setup as shown in Fig. The intensity of the interference patterns will decrease for longer propagation distances. In order to see the changes clearly, the brightness of the images in the figure has been adjusted to the same level.
From Fig. The spatial coherence value increases with the propagation distance. On the other hand, for the same propagation distance but different emitting sizes, the spatial coherence values show a similar trend as that in Fig. As the range of the emitting size is much larger in Fig. In this section, we study the corresponding holographic reconstructed images for the change in image sharpness. The experimental setup is shown in Fig. The experiment results are shown in Fig. In Fig. The similar pattern in central symmetric to the reconstructed image is the conjugated image, which has lower brightness.
The zero order locates in the center of the replay field, which is due to unmodulated light. It is the imaging of the emitting area of the LED, which can be observed in Fig. It can be found that as the opening diameter of the adjustable shutter decreases, the size of the zero order decreases and the sharpness of reconstructed image increases. We have measured the spatial coherence of these light sources and normalized them based on the value of DPSS laser, which is 0.
The reconstructed images of the same target image and the analysis results are shown in Fig. To evaluate the speckle, we define the speckle contrast C as the standard deviation of the intensity fluctuation to the mean intensity value in the area of interest:. As shown in Fig. The speckle contrast values are listed in Table 1 , the data has been normalized based on the speckle contrast of DPSS, which is 0.
On image sharpness, the features in the reconstructed images are all distinguishable for the different light sources in use. To make the results comparable, LED sources have been spatially filtered and all the images are normalized to the same brightness level.
To evaluate the image sharpness, we choose the same area of interest containing one edge of the square pattern, as shown in Fig. We calculate the mean intensity value of the edge, and define it as the edge intensity profile.
The ideal edge intensity profile should be a step function, but the actual one is not. The actual edge intensity profile will be the convolution of the ideal step function with a point spread function PSF. The normalized image sharpness value is shown in Table 1. As we discussed previously, the sharpness of the reconstructed images in holographic displays are mostly influenced by the spatial coherence, while the speckle are mostly influenced by the temporal coherence.
According to the data in Table 1 , we plot the relation between temporal coherence value and speckle contrast value in Fig. It can be found that the temporal coherence values of these light sources are quite different. The speckle contrast value and the temporal coherence value are in linear relation.
It is shown in Eq. Therefore, we can see the speckle contrast value is directly proportional to the temporal coherence value, as shown by the experiment results in Fig. For spatial coherence, to achieve distinguishable holographic reconstructed images, the spatial coherence values of these sources are in a rather high range from 0. In this case, if we take a look at Fig. Meanwhile, from Eq. Therefore, under these conditions, we would expect a directly proportional relationship between the spatial coherence value and the image sharpness value, which is confirmed by our experimental results as shown in Fig.
Coherence property of a light source can be characterized by its temporal coherence and spatial coherence values, respectively. Image sharpness and speckle are influenced by both temporal coherence and spatial coherence of the light source in use.
It is found that the image sharpness value is linear proportional to spatial coherence value, while the speckle contrast value is linear proportional to the temporal coherence value. Temporal coherence is decided by the intrinsic spectrum bandwidth of the light source and it can be improved by filtering the spectrum of the light source. On the other hand, spatial coherence is influenced by the size of the light source and the propagation distance in use, it can be improved by changing the size of the utilized light emitting area or the light propagation distance.
For example, in an LED based holographic display system, a spatial filter is often applied to reduce the utilized size and increase the spatial coherence of the LED source. However, improving either the temporal coherence or the spatial coherence of a light source by external means is at the cost of the reduced light intensity hence the reduced light efficiency.
Consequently, a light source with high spatial coherence and low temporal coherence is ideal for a holographic display in order to obtain high quality images with good sharpness and minimum speckle. LEDs with a broad spectrum can also be used to reconstruct holographic images with less speckle, but it has to be spatially filtered for reconstructive sharp images.
Otherwise there will be significant reductions in the energy efficiency and brightness of the reconstructed images. By selecting suitable levels of temporal and spatial coherences of a light source respectively, it is possible to optimize the produced image quality between uniformity and sharpness quantitatively. The corresponding speckle level can further help to determine the range of intensity variation due to the light coherence and hence the safety power level for a given light sources when viewing the produced images by human eyes directly.
For future work, we will investigate the ways to improve the spatial coherence of an LED while maintaining its good light efficiency. We will also consider investigating the impact of different coherence properties on the quality of star imaging for better positioning and tracking 39 , Choi, K.
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