Ralf Widenhorn, Lars Mündermann, Armin Rest, and Erik Bodegom, "Meyer-Neldel rule for dark current in charge-coupled devices," J. Appl. Phys. 89, 8179 (2001) pdf Ralf Widenhorn,  Morley M. Blouke, Alexander Weber, Armin Rest, and Erik Bodegom, "Temperature dependence of dark current in a CCD," Proceedings of the SPIE Vol. 4669, 193 (2002) pdf Ralf Widenhorn, Armin Rest, and Erik Bodegom, "The Meyer-Neldel rule for a property determined by two transport mechanisms," J. Appl. Phys. 91, 6524 (2002) pdf Armin Rest, Lars Mündermann, Ralf Widenhorn, Erik Bodegom, and T. C. McGlinn, "Residual images in charged-coupled device detectors," Rev. Sci. Instrum. 73, 2028 (2002) pdf Ralf Widenhorn, Erik Bodegom, "Interpreting fitting parameters," Proceedings of the second edition of the Colloquium "Mathermatics in engineering of numerical physics", Bucharest, 26 (2002) Ralf Widenhorn, Erik Bodegom, "Interpreting fitting parameters," Selected works of computer aided applied sciences, vol. 2, Bucharest, 595 (2002) Ralf Widenhorn,  Alexander Weber, Morley M. Blouke, Albert J. Bae, and Erik Bodegom, "PSF measurements on back-illuminated CCDs," Proc. of SPIE 5017, 176 (2003) pdf

Diffraction gratingformula

A diffraction grating is an optical element, which separates (disperses) polychromatic light into its constituent wavelengths (colors). The polychromatic light incident on the grating is dispersed so that each wavelength is reflected from the grating at a slightly different angle. The dispersion arises from the wavefront division and interference of the incident radiation from the periodic structure of the grating.

These influence the choice of grating line density, blaze angle/wavelength, master (different masters for a given line density and blaze angle yield different efficiency and polarisation characteristics) and grating size.

William C. Porter, Bradley Kopp, Justin C. Dunlap, Ralf Widenhorn, and Erik Bodegom, "Dark Current Measurements in a CMOS Imager," to be presented at Electronic Imaging 2008

Diffraction gratingformula wavelength

where: n is the order of diffraction, λ is the diffracted wavelength d is the grating constant (the distance between successive grooves) θi is the angle of incidence measured from the normal and θd is the angle of diffraction measured from the normal. The diagram above shows the orders of the diffracted wavelength. As well as positive orders, light can also be diffracted in the opposite direction (i.e. n = -1, -2 etc.) Higher orders may also appear, but these decrease in intensity. Usually the first order lines (n=1 or n=-1) are the most intense.

Diffraction gratingexamples

The dispersion and efficiency of a grating are dependant on the distance between adjacent grooves and the groove angle. Gratings are generally better than prisms - they are more efficient, they provide a linear dispersion of wavelengths and do not suffer from the absorption effects that prisms have which limits their useful wavelength range.

Ralf Widenhorn, D.A. Iordache, Erik Bodegom, “New Meyer-Neldel relations for the depletion and diffusion dark currents in some CCDs,” with , International Semiconductor Conference, 2004 Proceedings 2, 363 (2004) pdf

A.J.P. Theuwissen, M.F. Snoeij, X. Wang, P. R. Rao, E. Bodegom, “CMOS Image Sensors for Ambient Intelligence,” in “AmIware,” eds. S. Mukherjee et al., Springer, 125-150 (2006)

Diffraction gratingexperiment

Matthias. Loch, Ralf Widenhorn, and Erik Bodegom, “Infrared response of charge-coupled devices,” Proc. of SPIE 5677, 201 (2005) pdf

Diffraction gratingPDF

Diffraction gratingdiagram

Ralf Widenhorn, D.A. Iordache, Erik Bodegom,“Interpreting fitting parameters of temperature dependence of dark currents in some CCDs,” International Semiconductor Conference, 2005 Proceedings 2, 327 (2005) pdf

Reflectivediffraction grating

Andor’s new Mechelle ME5000 Echelle spectrograph has been designed to provide simultaneous recording of a wide wavelength range (200-975 nm) in one acquisition. It has no moving…

Ralf Widenhorn, Armin Rest, Morley M. Blouke, Richard L. Berry, and Erik Bodegom, “Computation of Dark Frames in Digital Imagers,” Proc. of SPIE 6501, 650103 (2007) pdf

Andor’s Kymera 193i spectrograph has been designed with research-grade performance, versatility and ease of use in mind. The ‘intelligent’ motorized adaptive focusing allows access…

The Andor Shamrock SR-500i imaging spectrometer is based on Czerny-Turner optical design. The optimized optical design provides exceptional performance for multi-track Spectroscopy.…

Ralf Widenhorn,a,b Ines Hartwig,a Justin C. Dunlap,a and Erik Bodegom, "Measurements of dark current in a CCD imager during light exposures," to be presented at Electronic Imaging 2008

What isdiffraction gratingin Physics

The Andor Shamrock SR-750 is based on Czerny-Turner optical design. The Shamrock is available as a pre-aligned detector/spectrometer option allowing for seamless integration of software,…

The dispersed light is then re-imaged by the spectrograph and the required wavelength range is directed to a detection system. Gratings consist of equally spaced parallel grooves, formed on a reflective coating and deposited on a substrate. The shape of the grooves (blaze angle) influences what wavelength range the grating is best optimised for.

Ralf Widenhorn, M. Fitzgibbons, Erik Bodegom, “The Meyer-Neldel rule for diodes in forward bias,” J. Appl. Phys. 96, 7379 (2004) pdf

Expected spectral resolution and simultaneous bandpass are also influenced by how light is coupled into the spectrograph, the central wavelength of interest and associated grating “working angle”, as well as the detector pixel array format at the output plane. Some of these trade-offs can be assessed with the Andor resolution calculator for Kymera and Shamrock Czerny-Turner spectrographs.