Calculating the focal length of a concave mirror computerically using mathematical algorithms using MATLAB
DOI:
https://doi.org/10.31185/wjps.498Keywords:
focal length . concave mirror. digital imageAbstract
This study proposes the use of digital image processing technology to determine the focal lengths of simple concave mirror , as well as spherical mirrors. This method is simpler, faster to implement, and more accurate in calculating the focal length by taking several pictures at different distances for the image formed by the lens, then calculating the least point spread function for these pictures at that distance to determine the best image. In this work Image No. (7) represents the image that carries the least (psf) that was determined by algorithms and special mathematical equations through the (Matlab) program, then the focal length is calculated by employing algorithms and mathematical equations specific to calculating the focal length. A comparison was made with the traditional method by taking measurements of a group of students at the Optics laboratory of University of Wasit, College of Science (which depends on view to choose the best image). This method has proven to be superior in measuring the focal length of lenses. A statistical analysis was conducted for these measurements for the group of students and it was found that there was differences measurements with an error rate, which confirms the feasibility of this method in terms of measurement accuracy and time saving. Experimental results have confirmed this.
References
J. W. R. Chong, K. S. Khoo, K. W. Chew, H. Y. Ting, and P. L. Show, "Trends in digital image processing of isolated microalgae by incorporating classification algorithm," Biotechnology Advances, vol. 63, p. 108095, 2023.
R. Kingslake, Ed., Applied Optics and Optical Engineering V6, vol. 6. Elsevier, 2012.
E. Keren, K. M. Kreske, and O. Kafri, "Universal method for determining the focal length of optical systems by moiré deflectometry," Applied Optics, vol. 27, no. 8, pp. 1383-1385, 1988.
S. Trivedi, J. Dhanotia, and S. Prakash, "Measurement of focal length using phase shifted moiré deflectometry," Optics and Lasers in Engineering, vol. 51, no. 6, pp. 776-782, 2013.
K. V. Sriram, M. P. Kothiyal, and R. S. Sirohi, "Direct determination of focal length by using Talbot interferometry," Applied Optics, vol. 31, no. 28, pp. 5984-5987, 1992.
P. Singh, M. S. Faridi, C. Shakher, and R. S. Sirohi, "Measurement of focal length with phase-shifting Talbot interferometry," Applied Optics, vol. 44, no. 9, pp. 1572-1576, 2005.
S. Rasouli, Y. Rajabi, and H. Sarabi, "Microlenses focal length measurement using Z-scan and parallel moiré deflectometry," Optics and Lasers in Engineering, vol. 51, no. 12, pp. 1321-1326, 2013.
F. Lei and L. K. Dang, "Measuring the focal length of optical systems by grating shearing interferometry," Applied Optics, vol. 33, no. 28, pp. 6603-6608, 1994.
J. Dhanotia and S. Prakash, "Focal length and radius of curvature measurement using coherent gradient sensing and Fourier fringe analysis," Optik, vol. 124, no. 15, pp. 2115-2120, 2013.
C. J. Tay, M. Thakur, L. Chen, and C. Shakher, "Measurement of focal length of lens using phase shifting Lau phase interferometry," Optics Communications, vol. 248, no. 4-6, pp. 339-345, 2005.
J. Yang, L. Qiu, W. Zhao, and H. Wu, "Laser differential reflection-confocal focal-length measurement," Optics Express, vol. 20, no. 23, pp. 26027-26036, 2012.
C. Y. Han et al., "Measurement of focal length and radius of curvature for spherical lenses and mirrors by using digital-grating moiré effect," in Photonics, vol. 8, no. 7, p. 252, Jul. 2021.
M. De Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform," Optics Communications, vol. 136, no. 5-6, pp. 370-374, 1997.
J. Yang, L. Qiu, W. Zhao, R. Shao, and Z. Li, "Measuring the lens focal length by laser reflection-confocal technology," Applied Optics, vol. 52, no. 16, pp. 3812-3817, 2013.
M. I. Malik, Z. H. Idan, and K. A. Assaf, "Study the magnetization of water using digital camera and laser beam," in IOP Conference Series: Materials Science and Engineering, vol. 928, no. 7, p. 072099, Nov. 2020.
S. H. Shahad, M. I. Malik, and H. A. Al-Dabbagh, "Land use and land cover study of Al-Kut city, Iraq using Sentinel-2 images by supervised classification techniques," in AIP Conference Proceedings, vol. 2834, no. 1, Dec. 2023.
R. C. Gonzalez and R. E. Woods, Digital Image Processing, Global Edition. Pearson Education Canada, 2017.
S. J. G. Hargis, P. L. H. D. Garza, and B. M. T. Davis, "Quantitative evaluation of point spread functions in optical microscopy," Journal of Microscopy, vol. 209, no. 3, pp. 261-273, 2003.
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