Mean square error (MSE) is used to detect variations in the period between a pair of self-images formed at two different Talbot planes of a circular grating (CG) using a beam splitter in a conventional collimation testing setup. By varying the position of the collimator with respect to the point source, the collimation state of the input beam is varied and the computed MSEs are analyzed to deduce the collimation state. The minimum value of the MSE indicates beam collimation. For equal sized images, the MSE relates to the sum of the squared difference between spatially correspondent pixel values of the images. Since comparison of the spatial information takes place at the pixels’ level, any small spatial shift between patterns of the two self-images due to collimation error is detected with precision. The CG, comprising concentric circular structures, offers added advantage in terms of error-free alignment, which otherwise is error prone and cumbersome with widely used linear gratings. It is well known that self-images formed with circular grating have good fidelity with less optical distortions and irregularities, especially at distant Talbot planes. Also, the self-images formed with circular gratings are less affected by lens aberrations, tilts, misalignments, etc. Higher sensitivity in beam collimation is achievable, as self-images of a CG can be recorded at widely separated Talbot planes, and analyzed using an algorithm which is more responsive toward any minute difference between them. The suggested method is promising for a quick collimation setting with good accuracy and enhanced sensitivity.

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This communication reports an investigation undertaken towards setting collimation of an optical beam using a self-imaging technique and histogram error (HE) based approach. The beam under test illuminates an amplitude type Ronchi grating. After the grating, a beam splitter is placed such that the grating’s self-images are formed in two perpendicular directions, at the different Talbot planes. The images are then recorded using two identical CCD cameras. Towards implementing a HE based algorithm, first, element-by-element subtraction of the normalized histogram of both self-images is computed. Next, the sum of the elements of the resultant image matrix is determined. Finally, the square of the sum yields the HE. HE provides an estimate of the collimation errors in the beam. For an incident collimated beam, the self-images recorded at different Talbot planes have identical unit magnification with respect to the grating; however, when the beam diverges or converges, the size and fringe width of self-images are differentially magnified or demagnified. Hence, when the beam is collimated, the HE is minimum. For the decollimated beam, the value of HE is higher, and increases as the decollimation errors increase. Using the proposed method, we could set the collimation position to a resolution of 1 μm, which relates to ±0.22 μ radians in terms of collimation angle (for a lens of focal length 300 mm and diameter 40 mm). Experimental results conclusively establish the viability of the technique. Good accuracy and precision in the measurement have been achieved.

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