M77781A
MS257
™ USB/RS232
MONOCHROMATOR AND SPECTROGRAPH
60
11 APPENDIX A - BASIC GRATING INFORMATION
F-Number
The F number is the ratio of the focal length to the limiting aperture. The limiting aperture is usually the
grating rather than the collimating mirror. F = 1 / (2 x NA). The smaller the F number, and the larger the
numerical aperture, the greater the amount of light collected. However, as the F number decreases, the
resolution deteriorates due to increased aberrations. This is compensated for by the instruments size and
mirror specifications. The F number is not a fixed value and changes with grating position. As the grating
rotates from a near normal (perpendicular) position, the effective aperture decreases and the F number
increases.
The specified F number of the MS257 is not as defined as one would first expect. The F number is
correctly defined as focal length / aperture diameter. However when the aperture is a rectangular grating,
what constitutes the diameter? Oriel Instruments solves this problem by using a diameter which would
give the equivalent area to the grating. For example: the effective F number of the Oriel 77781 is
calculated by using the focal length of 220 mm, and grating size of 50 mm square. The grating has an
area of 2500 sq. mm. The diameter of a circle with the same area would be 56.4 mm. The F number
would then be 220 / 56.4, i.e. 3.9. This is still considered to be an approximation since it assumes that the
entire grating surface is being used and that it is perpendicular to the incident beam, which is rarely the
case.
The Grating Equation
A typical diffraction grating consists of a substrate with a large number of parallel grooves ruled or
replicated in its surface and over-coated with a reflecting material such as aluminum. The quality and
spacing of the grooves are crucial to the performance of the grating, but the basic grating equation may
be derived by representing a section through the grating surface normal to the ruling direction as a saw
tooth pattern, shown in Figure 22.
Figure 22: Diffraction Geometry of a Plane Reflection Grating
