Designing a High Resolution Fiber-Fed Spectrograph for Solar Observations Edmond Wilson Brennan Thomason Stephanie Inabnet Tamara Reed Harding University

Project Goal Design a spreadsheet program to aid in optimizing the light throughput of a Czerny- Turner Spectrograph fed by an optical fiber

Czerny-Turner Monochromator Configuration

The model for our instrument is based on the discussion in Chapter 1 of the book, Guide for Spectroscopy, by Jobin Yvon/SPEX, Figure 1 below was created from Figure 3 in the book, with errors in the original figure corrected. Although the light path of a Czerny-Turner spectrometer is usually folded, mathematically, it can be treated as if the light path were arranged linearly without changing the results.

Equivalent Optical Path for Czerny-Turner Spectrometer

Begin with a grating…. Plane Grating Dimensions Richardson Grating Laboratories, Grating Model Number 290-R Given Enter Diffraction Order to Be Used in Calculations, k1Given Enter height of grating in mm, h G 58Given Enter width of grating in mm, w G 58Given Enter thickness of grating in mm & inches6Given Enter groove density of grating in grooves/mm, n1800Given Enter Blaze wavelength in Littrow configuration in nm500Given Enter Nominal blaze angle in degrees26.7Given

Collimating Mirror Next Collimating Mirror Dimensions Enter parabolic mirror diameter in mm64.00Given Enter parabolic mirror focal length in mm320.00Given Parabolic mirror focal length in inches12.60Calculated Enter parabolic mirror edge thickness in mm19.10Given Aperture, f/# (Calculated)5.00Calculated

Camera Camera Mirror Dimensions Enter parabolic mirror diameter in mm64.00Given Enter parabolic mirror focal length in mm320.00Given Parabolic mirror focal length in inches12.60Calculated Enter parabolic mirror edge thickness in mm19.10Given Aperture, f/# (Calculated)5.00Calculated

Slit Parameters Slit Dimensions Enter Fixed Slit Height in mm, h0.2987Given Enter Fixed Slit Width in µm, w =bandpass/dispersion, mm15Given Spectral Bandpass desired, nm0.5

Fiber Parameters Enter the diameter of the fiber in µm1000Given Enter numerical aperture of fiber0.22Given Length of Fiber Given

Begin the Calculations Spectrometer Parameters Enter D v in degrees12.52Given Enter L A in mm (L A = F, Focal Length of Spectrometer)320.00Given Grating Area in mm Calculated α λ, value of α in degrees at the wavelength of interest15.39Calculated β λ, value of β in degrees at the wavelength of interest39.39Calculated f/# of spectrometer5.00Calculated NA s is the numerical aperture of the spectrometer0.1Calculated f/# of fiber2.5Calculated NA f is the numerical aperture of the fiber0.22Given

Complete Optical Path Optimization for a Czerny- Turner Spectrograph that Employs a Fiber Optic Cable to Supply Light to the Entrance Slit S =7.85E-01mm G =1.19E-01mm 2

Step 2. Calculate the entendue, G, of the spectrometer Step 2a. Calculate the entendue of the spectrometer assuming a bandpass of 0.5 nm at 500 nm λ =600nmGiven BP =0.5nmGiven n =1800grooves/mmGiven k =1Given D V = 12.25DegreesGiven L A = F = L B =647.7mmGiven GAGA 3364mm 2 Calculated(G8 x G9) α 600 =15.39DegreesCalculated β 600 =39.39DegreesCalculated f/# spectrometer =5.0Calculated(G54) NA s =0.1Calculated f/# fiber =2.3Calculated NA f =0.22Given h =3.00mmGiven

Calculate entrance slit width and area =0.5829mm = mm 2 Calculate exit slit width mm Finally, calculate G of the spectrometer 1.40E-02spectrometer 1.19E-01fiber

Step 3. Re-image light from fiber to match it with the entendue of the monochromator so that the loss of photons and effect of stray light is minimized. This involves choosing Lens L 1 in Figure 1. This is somewhat arbitrary. You must choose a focal length and diameter for lens L 1

Solve for p and qp =145mm (q = M x p)q =320mm Solve for d, diameter of lens L 1 d =64mm Solve for d, diameter of Lens L 1 d =64mm Thin lens equation Therefore, all the light from the fiber is collected by a lens, L 1, with an object distance of p mm and will project an image of the fiber core on the spectrometer entrance slit q mm from lens, L 1

Solve for d, diameter of lens L 1 d =64mm Solve for d, diameter of Lens L 1 d =64mm Therefore, all the light from the fiber is collected by a lens, L 1, with an object distance of p mm and will project an image of the fiber core on the spectrometer entrance slit q mm from lens, L 1

Acknowledgement Thank you! Arkansas Space Grant Consortium Montana Space Grant Consortium