What is a Littrow spectrograph?

     Traditionally spectrographs are constructed using a slit, a lens to collimate light, a grating, and a lens to focus light (the spectrum) onto the detector. Littrow spectrographs, to minimize cost, size, etc., use only one lens, which the light passes through twice. This lens collimates light entering the spectrograph from a slit and sends it to the grating; after the light is dispersed, the lens focuses the spectrum onto a camera chip.

     There are several reasons that I wanted to build a Littrow spectrograph. On the one hand, I was wanting to build a new spectrograph anyway, since I wanted higher resolution than I had with my classical spectrograph. I wanted to use this new spectrograph both with the Raman system I was creating (with applications in physical chemistry) and for use with astronomy (to be attached to my family’s 12 in. Meade telescope).

     These seemingly opposite applications restricted my options with building the spectrograph. Had I only wanted to use it for astronomy, I could have given it a focal ratio of 10 (the same of my telescope),  but I would have had to make small and compact enough to fit behind my Schmidt Cassegrain. Had I only wanted to use it with Raman, it could have been larger (with a Raman spectrograph there isn’t normally a lot of reason to be moving the system around a lot) and in general less compact, but the focal ratio needed to be lower—the Raman effect is faint enough that you want as much light as you can get. So in the end I did end up choosing to build a Raman spectrograph, because it offered the benefit of being small, high resolution, and being able to have a low focal ratio (~4.8) at the same time.

1.    Abstract

A Littrow spectrograph was constructed. A medium-format 200 mm lens was used as a combined collimation and camera lens. A body, utilizing a diagonal mirror, connected the lens with the camera. The modular design facilitated interchanging of the lens, camera, and grating holder with different models. An adjustable slit was created, with light entering through a standard SCT-thread adapter. The spectrograph could be mounted directly to the Raman head or used in other applications, including astronomy. The F/4.8 spectrograph had a resolution of 6650 and a spectral range of 58 nm with a 1200

l/mm grating. The spectrograph was tested with a consumer DSLR camera as well as a cooled CCD camera.

2.    Objective

To build a medium- to high-resolution inexpensive amateur Littrow spectrograph, using one lens as a joint collimation and camera lens, to be attached to the Raman head and a collecting device.

3.    Theory

 

      So what, exactly, is a spectrograph? Spectrographs output graphs of intensity versus wavelength, meaning that

they show the different wavelengths of a particular light source. The spectrograph generally incorporates a spectral dispersion device (a diffraction grating), the collimation lens, and the collection device (for me, a CCD camera).

     The double-slit experiment, introduced by Thomas Young in 1801, is perhaps the simplest example of a diffraction instrument. A beam of light is first passed through a small hole or slit to ensure coherence and then directed to two slits a small distance apart. A screen is placed a relatively far distance from the slit, whereupon interference fringes are observed. (20) The interference fringes are the result of constructive and destructive interference; bright fringes, for example, represent constructive interference, and occur where the difference in the path length for light traveling from the two different slits is a multiple of the wavelength.

 

Fig. 9 - Diagram of Double-Slit Experiment (drawn from 23)

 

d= distance between slits

r= path to point on screen

L= distance between slits and screen (d<<L)

 

It makes sense that the small difference in path length, dsinq, results in bright fringes when it is a multiple of l, The wavelength of the (assumed monochromatic) light is , where m is an integer. The intensity of the bright bands is determined by the strength of the electromagnetic field at each point, and thus is a function of the common amplitude, d, 0, and l.  

     It turns out that the equation describing a situation with many multiple slits, all a distance

d apart, is very similar to the one describing the double slit experiment (see next page):

 

,

 

where N is the number of slits and m/N is an integer. Diffraction gratings, often made by ruling aluminum-plated glass, are essentially multiple-slit interference instruments. For values of m larger than 0, d sin q is dependent on wavelength, which is why gratings diffract light into its component colors in such a beautiful manner.

     It is useful to know the resolving power, or resolution, of a spectrograph, or in other words, to know how close two lines of different wavelengths may be while still being differentiable. The equation for constructive interference is d sin q = ml. The equation for destructive interference is  where m/N is not an integer. If

for the first line, I can write the adjacent minimum equation (where m= m+l) by adding 1 to the numerator mN:

This makes sense because I am effectively adding l/N, and there is a destructive interference at each m multiple of  l/N. If the two wavelengths and their associated angles are denoted l and l’ and q and q’:

 

for θmax to =  θmin :

 

If I find the wavelength difference

I can then write Δλ in terms of λ alone and rearrange:

     λ  / Δλ  is defined as the spectrograph’s resolution.

     In a Littrow spectrograph, the light cone from the slit-focusing Raman lens hits the spectrographs slit (or simply diverges, in slitless operation) and is collimated by the lens. Thus the rays are parallel when they hit the grating. The grating is fitted in such a way that in one plane it acts like a mirror, diffracting the spectrum back through the lens, which focuses the spectrum on the focal plane of a camera plane behind the lens:

 

 

 

Fig. 10 – A successful Littrow spectrograph design by Christian Buil of France, used for astronomical spectroscopy (24). In the top diagram the grating acts like a mirror; in the bottom diagram it disperses the light across the CCD chip.

 

 

Fig. 11 – Another image of Christian Buil’s Littrow spectrograph (24).

 

     The spectrograph should probably use a 1200 lines/mm grating, since 600 lines/mm gratings would not give me the resolution I desire unless I had a very long focal-length (=> expensive) fast lens. Such a lens would have such a large diameter that the exit beam and grating would be larger than is pragmatic or affordable.

     To determine the size the grating needs to be- an important factor since large gratings quickly become very expensive- the diameter of the beam exiting the collimation lens must be determined. This diameter is dependant on the F-stop of the slit-focusing lens as well as the focal length of the collimation lens. My Raman system is F5, so I need a collimation lens preferably F5 or faster. The longest focal-length lens that can be reasonably carried by an amateur telesocope is on the order of 200-300 mm.

     The grating must actually be slightly larger than the diameter of the beam exiting the collimator, since it is at an angle. The resolution power of a spectrograph, as we saw earlier, is dependant upon the number of slits N- i.e. the number of grooves illuminated on the grating. Thus it is best when the entire grating is illuminated.

     Christian Buil uses Achromatic lenses to build Littrow spectrographs. Achromat lenses, as used in inexpensive binoculars, use two type of glass to cancel out optical aberrations of two wavelengths. Since camera lenses are often apochromats, which are corrected to focus at at three wavelengths. That would be a preferred solution. Since his spectrographs are made for F/10 telescopes, the achromats work fine, but the Raman system will work

better with a faster F#5 system with apochromatic lenses.

     The challenges in designing a Littrow with commercial lenses and cameras is that it is difficult to fit the small flat diagonal mirror that reflects light from the slit/focal plane between the camera and lens. CCD cameras would be best to use, since their flange-to-film distance (backfocus) is smallest.  Maurice Gavin (18) made a spectrograph using an off-axis telescope guider. I considered this also; but it seemed like the tiny  .25” (6.35mm) mirror/prism would be too small for the light cones required.

     The question, then, is what focal-length lens is ideal. We have already established that f/5 = D in an f/5 system, where D is the diameter of the collimator beam. If I know that I can buy a 50 mm grating, maximum, I can calculate what the diameter of the collimator beam can be (largest possible) if  know the angle the grating will work at.

 

 

Fig. 12 – No matter what the focal ratio of the collimation lens is, the actual focal ratio is

determined by the focusing lens of the Raman system on the other side of the slit.

 

 

 

Fig. 13 - Drawing from www.edmundoptics.com/techSupport/DisplayArticle.cfm?articleid=285. A diffraction grating is analygous to a screen with many hundreds of slits. The equation above, fundamental to the entire science of spectroscopy, is called the grating equation.

 

For the double-slit experiment:

 

D = Max collimator beam

GW = Grating Width

(d ≥ D )

d= GW cos θ

 

What, then, is θ? θ is the angle between the center axis and the line perpindicular to the grating. I can actually calculate this angle, since I know that I want to use a 1200 lines/mm grating, using an equation called the grating equation (see above), very similar to the equation describing a system of multiple slits:

where   λ is the wavelength in mm

            k is the order (-1 or 1 for me)

n is the number of grooves per mm

α = angle of incidence

β = angle of diffraction.

 

In a Littrow spectrograph, this equation is much simplified, as  α = β = θ: 

If we plug this angle back into d =  GW cos θ, and if d = D, and if f = 5D (see calculations), then the collimator lens should have a focal length of  ≈ 230 mm. For feasibility, I will select a lens of 200 mm. This means that the exit beam will be 40 mm, and will leave about 6 mm of lines on the grating left unused. This is actually a bonus; it will give me some leeway during alignment.

     I know that I need a 200 mm collimation/camera lens, ideally. The question, then, is what camera to use. I have an SBIG ST-7e CCD camera my family uses for astronomy (ideal because it is cooled and very sensitive) and a Canon digital camera. The deciding factor between the two cameras is range; the Canon chip is 22 mm long and the SBIG camera chip is 6.9 mm.

     The spectral range is Å of a spectrograph is calculable by multiplying a value called the plate factor or linear dispersion (in Å /mm) by the chip size in mm (Å/mm*  mm = Å). The linear dispersion, or P, is given by

 

If range= Pl, where l is the length of the chip, range= 264 A for the CCD and 843 A for the Canon. Since Raman spectroscopy is best with  500 A, and astronomical spectroscopy is best with as large a range as possible, the SBIG CCD is unrealistic and I will have to use the Canon camera.

     I found the Canon EOS 300D Digital Rebel (my camera) has a flange-to-film distance of 44 mm (http://bobatkins.photo.net/photography/eosfaq/manual_focus_EOS.html). At http://www.a1.nL/phomepag/markerink/mounts.htm, I found a list of lenses from Bronica, Hasselblad, Mamiya and Pentax that had 75-112 mm flange-to-film distances. These were medium format camera lenses, and more feasible than Canon lenses because of the increased flange-to-film distance. If I could make an adapter to attach such a lens to my Canon camera, I could probably fit the diagonal inside.

     Most of the lenses, unfortunately, were very expensive; but when I researched prices of used models of various websites, I found that Pentax 6x7 cm film sizes lenses were very cheap at KEH.com camera brokers. I ordered a “bad-condition” lens, 200 mm focal length, for $109.00.

Realizing it would be hard to mount the lens, I ordered a Macro adapter for $35. It is used for close-up photography, to space the lens out from the camera. I hope that it will be possible to use the flange/bayonet instead of making a new one.

 

 

Fig. 14 - Photo of the Pentax lens I bought from (26).

 

Flange-to-film Pentax lens distance  = 84.95 mm

Camera flange to chip distance         =  44.00 mm

T-thread adapter thickness                =  15.24 mm

  Total room for SCT adapter (slit)/diagonal mirror section = 25.71 mm.

 

     The SCT adapter will be 0.75” on the outside, since I have a ¾” drill bit. I will use a Schmidt-Cassegrain telescope adapter (SCT) threaded ring from an old flip mirror I built a spectrograph from in 2004. I will make a slit holder to go on the SCT adapter. I will make a new SCT adapter to connect the spectrograph to the telescope or Raman system.

     A further advantage of the Pentax lens is that the infinity side has 67 mm filter threads. Since I could not make threaded parts, I made the grating holder fit onto the 67 mm filter. I found that Epperson Photo in Oklahoma City has filters for $12.

 

Photo from (27).

 

 

I ordered a 1200 lines/mm 50 mm ruled grating from Edmund Optics.

 

Curve 2

6.    Data Analysis

 

     Spectra were calibrated with a mercury lamp, and the observed wavenumbers for various lines in the spectra correlated very well with published wavenumbers. The resolution of the Littrow spectrograph with the 1200 lines/mm grating was about 7000, and the range was about 300 Angstroms, which turned out to be enough to cover most of the desired spectral range with Raman.

7.    Conclusions

 

     The Littrow spectrograph proved to be very difficult to construct due to the complicated process of optical alignment associated with the diagonal mirror between the collimation lens and the camera chip. The difficulty associated with accounting for the small backfocus of my digital camera proved to be a severe problem. The Littrow spectrograph produced spectra that were higher resolution than the classical spectrograph constructed in my previous project; however, all in all, I would say that the difference in resolution and spectral dispersion were not worth the added trouble of building and collimating the new spectrograph.

8.    Acknowledgements

     I would also like to thank Alan Holmes and the Santa Barbara Instrument Corporation (SBIG) for letting me borrow an ST-10 CCD camera for use with my project. I would like to thank the IAPPP (International Amateur Photoelectric Photometry) and the AAS (American Astronomical Society) for granting me and my previous partner Sarah Howell the Richard D. Lines award last year, which helped to finance my project this year. I would also like to thank Mr. Jeffrey Baughman for helping me with all of the advice he offered me concerning my project. I would most like to thank my parents for their support, specifically my dad, who taught me how to use AutoCAD to design my spectrograph and instructed me in the difficult process of machining the parts for my spectrograph.

9.    Bibliography

 

1.      Abramowitz, M., & Davidson, M. (2004). Molecular Expressions Microscopy Primer: Specialized Microscopy Techniques: Flourescence Filters. Retrieved November 10, 2005, from http://microscope.fsu.edu/primer/techniques/fluorescence/filters.html.

2.      Anderson, Larry (2000). Raman Spectroscopy. Retrieved November 23, 2005, from http://carbon.cudenver.edu/public/chemistry/classes/chem4538/raman.htm.

3.      Beaucage, G. Infrared Spectroscopy and Raman Scattering (1998). Retrieved January 2, 2006 from http://www.eng.uc.edu/~gbeaucag/Classes/Analysis/Chapter5.html.

4.      Bowdoin. Orientation and Intermolecular Forces (n.d.). Retrieved December 23, 2006, from http://academic.bowdoin.edu/courses/f01/chem225/chem225b/Polarity/Orientation.shtml.

5.      Brief description of raman scattering. http//www.omegafilters.com/index.php?page = omegatext/prod_raman_scatter.

6.      Buil, Christian. (n.d.) The Littrow Spectrograph. Retrieved Novemeber 4, 2005, from http://www.astrosurf.com/buil/us/spectro8/spaude_us.htm.

7.      Clarke, R., Londhe, S., Premasiri, W., & Womble, M. (1999). Low-Resolution Raman Spectroscopy: Instrumentation and Applications in Chemical Analysis [Electronic version]. Journal of Raman Spectroscopy, 30, 827-832.

8.      Colthup, Norman B. (1990). Introduction to Infrared and Raman Spectroscopy. San Diego, CA: Academic Press.

9.      DeGraff, B., Hennip, M., Jones, Julie, Salter, C., & Schaertel, S. (2001). An Inexpensive Laser Raman Spectrometer Based on CCD Detection [Electronic version]. Chem. Educator, 7, 15-18.

10.  Drug detection using Raman spectroscopy (2004). Retrieved November 23, 2005, from www.renishaw.com/UserFiles/acrobat/UKEnglish/SPD-AN-097.pdf.

11.  Gavin, Maurice. Stellar spectrograph (2003). http://www.astroman.fsnet.co.uk/newspec.htm.

12.  Ferraro, J. & Nakamoto, K. (1994). Introductory Raman Spectroscopy. San Diego, C.A.: Academic Press, Inc.

13.  Filter Types for Raman Spectroscopy Applications (2005). Retrieved November 23, 2005, from http://www.semrock.com/Catalog/Raman_filtertypes.htm.

14.  Forensics Research at NUI, Galway. (n.d.) Retrieved November 23, 2005, from http://www.nuigalway.ie/chem/AlanR/ARyderPage4.html.

15.  Freck, Roger. (2006). Interview of sorts with Dr. Freck of the University of Oklahoma physics department about theory behind Raman spectroscopy on February 9, 2006.

16.  Harris, D. & Bertolucci, M. (1989). Symmetry and Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy. Mineola, N.Y.: Dover Publications, Inc.

17.  Horiba Jobin Yvon. An Introduction to Raman Spectroscopy (2006). Retrieved February 20, 2006, from http://www.jobinyvon.com/usadivisions/raman/tutorial1.htm.

18.  In situ Planetary Raman Spectroscopy. (n.d.) Retrieved September 29, 2005, from Washington University in St. Louis web site: http://epsc.wustl.edu/haskin-group/Raman/applications.htm.

19.  Kaiser Optical Systems, Inc. Raman Tutorial (1998). Retrieved January 18, 2006, from http://nte-serveur.univ-lyon1.fr/nte/spectroscopie/raman/h1tuto~1.htm.

20.  Physics, 3rd edition. (1999). Addison Wesley Longman, Inc.

21.  Raman Spectroscopy - An Overview (2001). Retrieved November 23, 2005, from www.kosi.com/raman/resources/technotes/1101.pdf.

22.  Reinecke, Norbert. Spectroskopie (n.d.). Retrieved February 25, 2006, from http://www.pollmann.ernst.org/reinecke.htm.

23.  Tissue, Brian M. Raman Spectroscopy (1996). Retrieved January 18, 2006 from http://elchem.kaist.ac.kr/vt/chem-ed/spec/vib/raman.htm.

24.  Ward, A., Parker, A., Botchway, S., & Towrie, M. Development of Raman Tweezers (2001). Retrieved September 28, 2005, from www.clf.rl.ac.uk/Reports/2001-2002/pdf/95.pdf.

25.  Zholobenko, Vladimir. Molecular Spectroscopy Lecture (2001). Retrieved January 21, 2006, from http://www.keele.ac.uk/depts/ch/courses/p2_courses/chem202/202lec4w/sld001.htm.

 

 

home

Website by Mary Masterman

Please send questions or comments to marymast@gmail.com

Last updated June 9, 2006

 

Some of the pictures on this page have been taken from other websites, but have been cited.

If you have a problem with this please contact me and I will remove them.