Histogram error based algorithm for efficient collimation testing

Abstract

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.