Collimation testing using wedge plate lateral shearing interferometry and Fourier fringe analysis Jitendra Dhanotia, Shashi Prakash n Photonics Laboratory, Department of Electronics & Instrumentation Engineering, Institute of Engineering & Technology, Devi Ahilya University, Khandwa Road, Indore 452017, India article info Article history: Received 18 January 2011 Received in revised form 3 March 2011 Accepted 11 April 2011 Available online 29 April 2011 Keywords: Collimation Wedge plate Lateral shearing Fourier transform abstract For checking the collimation of an optical beam Fourier fringe analysis has been incorporated into the wedge plate interferometric setup. Typical interferograms corresponding to ‘in-focus’, ‘at-focus’ and ‘out-of-focus’ positions of an optical beam have been recorded. As per the testing procedure, FFT of the recorded interferometer is computed digitally, and necessary processing for direct determination of phase is undertaken. Finally, the phase data is unwrapped and plotted as a function of pixel position along the direction perpendicular to the shear. The slope of the phase provides the information regarding collimation position of the collimator. As the collimation position is detected by the direct measurement of the phase over the whole area of the interferogram, high accuracy, reliability and precision are achieved. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction In optical metrology, for almost all the applications there is a requirement of collimated beam. Methods have to be evolved for checking the degree of collimation of the beam. In past, several methods have been developed for checking the collimation of the optical beam. These methods are based on collimation testing using parallel plate shearing interferometry [1], Talbot interfero- metry [2–4], temporal coherence [5], wedge plate shearing inter- ferometry [6], optically active mediums [7], Lau interferometry [8], double prism [9], etc. Among these techniques, the wedge plate shearing interferometric technique has been observed to have the best accuracy, is simple and can be realized with the help of compact geometry. All the above mentioned techniques are based on the relative variation in type, width or inclination angle of fringes with respect to the collimation position. Since, these techniques are based on the visual inspection alone, the results obtained are not quantitative and are subject to vary based on the visual percep- tion of human senses. Also, the measurement characteristics of the techniques are relatively poor. As an alternative to these techniques, direct phase measuring technique, such as phase shifting method, has been reported [10]. It has tremendously improved the measurement characteristics in terms of accuracy, precision and sensitivity achievable. However, phase shifting test procedure requires specialized translation stage and recording of several interferograms to determine the phase. This makes the technique tedious and relatively cumbersome. In this paper, we report our investigations to be undertaken toward automated checking of the collimation position of colli- mating lens using wedge plate interferometry in conjunction with the Fourier transform technique. The experimental setup is very simple and uses a single wedge plate. The interferograms corre- sponding to different defocusing errors for the collimating lens were recorded and analyzed using the Fourier transform method. The accurate detection of collimation position with high accuracy has been achieved by determining the phase plots of the inter- ferograms. Only a single interferogram is required to extract the phase information and the phase plots. 2. Basic theory The theoretical treatment regarding the Fourier Transform method has been explained earlier [11]. Here, we briefly sum- marize it for ready reference. The recorded fringe pattern can be described by gðx, yÞ¼ aðx, yÞþ bðx, yÞcos½2pf ox x þ 2pf oy y þ Fðx, yÞ ð1Þ where a(x,y) is the background noise, b(x,y) is the variation in fringe visibility, F(x,y) is the phase information of interest and f ox and f oy are the spatial carrier frequency in the x and y directions, respectively. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optlaseng Optics and Lasers in Engineering 0143-8166/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2011.04.007 n Corresponding author. Tel.: þ91 731 2361116 7, þ91 9977186156; fax: þ91 731 2764385. E-mail address: sprakash_davv@rediffmail.com (S. Prakash). Optics and Lasers in Engineering 49 (2011) 1025–1031