in studying the interference of light through the Michelson interferometer the fringes pattern will appear in circular shape with the dark fringes from the center, my question is why the fringes are in the form of circle shape not straight line for example as in Young double slit experiment, it will be better for me to understand well if you provide a mathematical approaches with your answer, thank you.
This is because in the typical arrangement of a Michelson Interferometer, the wavefront of the interfering laser beams at the detector/screen is not perfectly flat, but rather having ever so slightly a curvature (large ROC) to it. This could be unintentionally introduced into the lens system (e.g. beam expander, collimator, etc.). As such you may observe circular or arc fringes, depending on the angle of your detector/screen. If you have a 'perfect system, then you would either have a destructive or constructive interference at 90-deg screen angle, or pretty linear fringe patterns at off-90-deg angles. The sensitivity of interference pattern to changes in wavefront shapes is the very principle applied in detecting imperfection in optical systems and also in the field of Adaptive Optics to design optical systems with active and realtime wavefront correction. It has also been used as wavefront sensors, for example, to measure the curvature of the cornea in laser-guided eye surgery for vision correction by provided the computer with the feedback signal needed to calculate where the laser should fire on the cornea to change/correct the corneal curvature.
Thank you Kin for your kind cooperation, but is there a mathematical approaches for the fringes being circle?
when i was your student in under graduate level you asked the same question of us, as i remmeber that time i could only found physical expaination for this phenomena and you gave me one mark ove all average
i wrote those above lines to you because this question give back many nice memorize to me when i tried to find this answer, when i spent many hours for thinking, searching, interperating, ask others,....etc.
now because of you i can say i have a great basic in optics
thanks for every things
Dear Othman
Thank you for your kind cooperation, I am still looking for the exact answer for this fundamental question especially the mathematical approaches to this phenomenon, thank you.
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