Mica transmission fringes
This figure shows a full calculation of the mica fringe pattern using the methodology presented by R. Swanepoel, 1983, J. Phys. E: Sci. Instrum. 16, 1214. (orange line). The observed data are shown as the blue line (visible JAZ spectrum) and the blue x (NIR NIRQUEST spectrum - which does not resolve the fringes below about 1100nm).
In the calculation, the absorption coefficient (giving the imaginary part of the refractive index) has been determined from transmission measurements (green line) of a thicker (0.63 ± 0.02 mm) mica flake.
For simplicity, I have used a value for n (the real part of the refractive index) which is a linear function of wavelength. This is not a very good approximation and should really be replaced by a more appropriate functional form. However, the model is a respectable fit to the data.
The black dots show the interference order calculated by the simple geometrical formula for transmission maxima (no phase change of pi as in reflection) are given by:
2 n d cos(beta) = m Lambda_t
where n is the refractive index (using the same linear function), d is the mica thickness, beta is the angle of refraction (inside the mica) = zero in this case, m is the order of the interference and Lambda_t is the wavelength of maximum transmission.
In this plot, the order, m, runs from 10 to 62.
This has been an interesting exercise for me in classical optics modelling and is, of course, very relevant for problems such as 'fringing' in CCD imaging.
Mica transmission fringes
This figure shows a full calculation of the mica fringe pattern using the methodology presented by R. Swanepoel, 1983, J. Phys. E: Sci. Instrum. 16, 1214. (orange line). The observed data are shown as the blue line (visible JAZ spectrum) and the blue x (NIR NIRQUEST spectrum - which does not resolve the fringes below about 1100nm).
In the calculation, the absorption coefficient (giving the imaginary part of the refractive index) has been determined from transmission measurements (green line) of a thicker (0.63 ± 0.02 mm) mica flake.
For simplicity, I have used a value for n (the real part of the refractive index) which is a linear function of wavelength. This is not a very good approximation and should really be replaced by a more appropriate functional form. However, the model is a respectable fit to the data.
The black dots show the interference order calculated by the simple geometrical formula for transmission maxima (no phase change of pi as in reflection) are given by:
2 n d cos(beta) = m Lambda_t
where n is the refractive index (using the same linear function), d is the mica thickness, beta is the angle of refraction (inside the mica) = zero in this case, m is the order of the interference and Lambda_t is the wavelength of maximum transmission.
In this plot, the order, m, runs from 10 to 62.
This has been an interesting exercise for me in classical optics modelling and is, of course, very relevant for problems such as 'fringing' in CCD imaging.