Assignment 1.Generally, monochromaters displaying high resolving power are required to contain long focal length optical components. However, an...
Assignment
1.Generally, monochromaters displaying high resolving power are required to contain long focal length optical components. However, an alternative to this is the incorporation of an Echelle grating which is then operated at higher orders of diffraction. Unfortunately, at these higher orders of diffraction, extensive order overlap is observed. To overcome this difficulty, a prism is sometimes included as a cross-dispersion element within the monochromater.
A. For such a cross-dispersing Echelle monochromater, with the following specifications, calculate the resolving power of this monochromater at orders 50, 75, 100, and 120 for wavelenths of 200 nm, 400 nm, and 700 nm. (Note: resolution is in each of two dimensions.)
Focal length 0.750 m
Grating width 9.60 cm
Grating height 4.60 cm
Diffraction angle 63.43
Groove density 79 grooves/mm
Prism angle 30
Prism material Fused Silica
Prism base 3.0 cm
Wavelength/nm______
200.0 400.0 700.0
Refractive Index 1.5505 1.4696 1.45515
Dispersion (of the material)
1.08258 1.12698 1.13086
B. Calculate the band pass of the instrument with vertical slit widths of 50, 100, and 200 m and horizontal slits of 10, 25, and 50 m (Hint: they are unrelated).
C. Determine the f/# of the monochromater.
D. Because the internal spherical mirrors of the monochromater are illuminated off-axis, astigmatic images would be predicted to be formed. With an off-axis angle of 3.0 degrees, compute the distance between the two resulting astigmatic images. Is that distance significant to prohibit the use of the monochromater (i.e., does the circle of least confusion exhibit tolerable blur)?
E. What would be the dimensions of a multi-point detector to enable the simultaneous measurement of the entire spectrum from 200.0 nm to 650.0 nm? Propose a detector for this purpose. What parameters would need to be changed to use a CCD camera with dimensions of 1.50 cm x 1.50 cm and detecting elements (i.e., pixels) with a separation of 15 μm, center to center?
