Basic spectrometer types - PDF Free Download

Spectroscopy

Basic spectrometer types Differential-refraction-based, in which the variation of refractive index with wavelength of an optical material is used to separate the wavelengths, as in a prism spectrometer. Interference-based, in which the light is divided so a phase-delay can be imposed on a portion. When the light is re-combined, interference between the two components is at different phases depending on the wavelength, allowing extraction of spectral information. The most widely used examples are diffraction grating, Fabry-Perot, and Fourier spectrometers. Heterodyne spectroscopy also falls into this category, but we will delay discussing it until we reach the submillimeter Bolometrically, in which the number of charge carriers generated when a photon is absorbed in the detector, or the energy of that photon, are sensed. These methods are widely applied in the X-ray.

Data Cubes In addition to spectral information, most spectrometers also provide at least some information about the distribution of the light on the sky. Where a full image can be obtained along with the spectral data for each point in the image, we imagine a three dimensional space called a data cube, with spectra running in the z direction and such that any slice in an x,y place produces an image of the source at a specific color. The ability of spectrometers to produce data cubes varies. Simple grating or prism spectrometers usually use a slit to avoid overlap of the dispersed beam sections and therefore only provide spatial information in one direction, that is they produce the x,z part of the data cube directly. To some extent this shortcoming can be mitigated with an image slicer or integral field unit (IFU) that rearranges the image of the source so part of it in the direction perpendicular to the slit can enter the spectrometer and be dispersed.

(2) ) ( 2 2 2 2 1 2 2 1 2 C B C B A n The simplest type of spectrometer is based on a prism. Just apply Snell s Law with a varying index of refraction to get dispersion. To get good optical performance requires the symmetric arrangement above.

Here is how a prism spectrometer might look. Why all the optics?

Consider the two lenses separately. The second one is the camera it works just like a camera! camera

The first one is the collimator. collimator camera Together they just reimage the telescope focal plane (to left) onto the detector array (to right). The focal lengths of the lenses determine the scale of the image, input compared with output.

To prevent mixing spatial and spectral information, we need to put a field stop at the telescope focal plane that limits the field of view along the direction of the dispersion. Since it is narrow, it is called a slit.

What determines the spectral resolution? A B If the used diameter on the camera lens is small, then the spectrum is imaged to a short length at the focal plane of the camera (heavy black line) and the spectral resolution is low.

Here is another version of the same concept:

If the used diameter on the camera lens is large, then the spectrum is imaged to a larger length at the focal plane of the camera (heavy black line) and the spectral resolution is higher. What determines the spectral resolution? A We can increase the used diameter by adjusting the optical design or by selecting a more dispersive material for the prism So the larger the used diameter of the camera lens, the higher the spectral resolution B

Increasing the diameter of the collimated beam tends to increase the used diameter of the camera lens. We can also improve the resolution by narrowing the slit.

What else can we do to increase the spectral resolution??

Nothing!!!!

Prism spectrometers are not very adaptable in design because we have to settle for the dispersive characteristics of transparent optical materials. More options are available if we use a diffraction grating in place of a prism. Here is such a spectrometer. Except for the grating, it is hardly changed!

How a grating works. Consider a series of slits illuminated by parallel light. The interference pattern that results will have an envelope due to the diffraction pattern of a slit, and within it will have constructive interference peaks at orders 0, 1, 2, etc. corresponding to 0, 1, 2 etc. wavelengths of retardation

(3) sin sin d i d p (6) sin sin sin sin 2) / ( sin 2) / ( sin ) ( 2 2 2 2 2 2 d d N a N a AA I (7) sin sin sin ) ( 2 2 0 2 w w I a I slit More mathematically (additional details in the book), the path difference between successive slits is leading to the interference pattern between slits of within the envelope of the diffraction of a single slit:

Diffraction Gratings To use this effect as a spectrometer, we want >> 0, that is we want to work at an order > 0. See equation (6) if = 0, the dependence disappears. But from equation (7), as grows, the intensity drops. To solve this problem, we replace the slits with a bunch of little tilted mirrors, all arranged parallel to each other. We now have a diffraction grating! Equation (3) becomes m d(sin sin ) (8) where we have substituted m for p, and m is the order. This is the famous grating equation!

Here is a real grating operated in different orders. Note also the polarization dependence.

Here is the entire optical system (schematically). We need to separate the orders, for example with a filter. The arrangement works best with the grating at a pupil. The spectral resolution is (see book for derivation), with the slit width: D (sin sin ) R 1 D cos (12)

At extreme illumination angles, anamorphic magnification lets the camera beam be significantly larger than the collimated beam.

This remains simple, just as we found for the prism spectrograph. For example, The resolution: 1.) goes inversely as the size of the telescope (assuming equal projected slit width); 2.) increases with increasing tilt of the grating; 3.) goes inversely as the field projected onto the sky, i.e., the slit width; and 4.) goes in proportion to the diameter of the beam delivered to the camera. In exchange for our designer disperser we have to separate its orders.

In addition, we have to learn how to make a grating. Here is an article by a very determined amateur on how to do so: http://www.britastro.org/iandi/manning1.htm But maybe it would be smarter just to order one from Richardson Labs. If so, you will probably get a replica cast from a grating that was actually ruled. Master gratings can also be manufactured holographically. In this case, an interference pattern is projected onto a light sensitive coating on the grating substrate. After exposure, this coating is developed to remove the unexposed regions, leaving a series of grooves. Because there is no mechanical removal of material, holographic gratings have low levels of scattering. However, it is difficult to blaze them as effectively as for ruled gratings and consequently they generally have lower efficiency.

Historic ruled gratings (used by Herzberg)

A modern ruled grating

A simple holographic grating made by exposing a periodic pattern on a photoresist and then using chemical methods to develop the resulting grooves:

Shimadzu process to blaze a holographic grating

Volume phase gratings use holographic techniques to produce a periodic variation of the index of refraction in the bulk of a transparent material. If these fringes are perpendicular to the surface, the VPG acts as a transmission grating. A VPG can have high efficiency and be packaged between glass plates to make it rugged.

VPH gratings have high efficiency, but relatively narrow spectral range (from TNG, Telescopio Nationale Galileo) Table 1: The main characteristics of the new VPH grisms installed on Dolores @ TNG. V390 V486 V510 V589 V656 V860 VHRV VHRR VHRI O3727 4000 HeII 4670 H? 4861 OIII 5007 Mg5200 Na D 5890 Ha 6563 Ca 8600 / / / gr/mm 1511 2040 1886 1600 1400 1060 566 660 685 Eff. Lmed 0.85 0.77 0.81 0.84 0.86 0.86 0.80 0.81 0.85 Lmin 3600 4550 4850 5590 6200 8100 4650 6200 7360 Lmax 4200 5000 5350 6200 6920 9100 6800 7800 8900 Rs 3100 5200 5100 4700 4550 4300 1480 2430 2950

Sometimes it is useful to have a way to disperse light without deflecting it. This can be done with a grism the deflection of the prism is countered by that of the grating. Placing a grism at the pupil in a suitably designed camera (and a slit in the focal plane) produces a spectrometer, albeit of modest spectral resolution.

Echelle gratings are another useful variant. They operate at high incidence angle and high order (50 100). They are commonly used in high spectral resolution instruments, and usually with some kind of cross disperser to get more than one order on the detector at a time.

Some standard spectrometer designs Ebert-Fastie perhaps the simplest overall optical arrangement

The Czerny Turner design separates the collimator/camera mirror into two to allow more flexibility, but is otherwise similar.

At high spectral resolution, it may be optimum to have the entrance and exit beams along the same optical path. This condition is called Littrow.

An modern spectrometer example: GMOS on Gemini

What s Inside the Box

Although it has lots of extras, it is basically a simple spectrometer. 0.36 1.1mm, 5.5 arcmin FOV

1 5mm, 3 arcmin FOV, 6.5-m telescope

What it looks like:

This one is not so simple because it has to reimage to get the right scale for its multi-aperture unit.

NIRSpec reimaged focal plane

And it uses all-reflective optics: the basic optical unit is a threemirror anastigmat (TMA), corrected for all major aberrations.

Here is the basic idea behind a TMA. Light comes from the left to a folded three-mirror telescope as we showed when discussing telescopes. The image is formed to the right. Although the full symmetric version (top) blocks the light, off axis it can work. Recall that these designs can correct all the low order aberrations over a reasonably wide field.

This instrument features multi-apertures via microshutters Coated with a magnetic film, each microshutter has an electrode on the shutter surface as well as on the back wall. A magnet is swept across the array, pulling each shutter toward the magnet. When the shutter is opened, a voltage potential is applied between the surface of the shutter and the back wall. This potential difference holds the shutter in the open position once the magnet has passed. Once all the shutters are placed in the open (or latched) position, the voltage potentials can be selectively removed from the shutters that need to be closed.

Grating Spectrometer Warts Grating spectrographs are subject to all the standard aberrations: spherical, coma, astigmatism. In many cases, slight degradations of the images are hidden because of the relatively large pixels and the effects of the slit and spectral dispersion. Distortion, however, is critical. The extreme f/numbers required for good matching of the pixels of the detector to the projected slit can result in a substantial level of distortion. Distortion must be corrected very carefully in data reduction. A key step in the analysis of spectroscopic data is to conduct a fit to the apparent wavelengths of lines from a calibration source and to correct the spectra for the indicated errors in the wavelength scale.

Ghosts There can also be optical issues associated directly with the grating. Periodic errors in the groove spacing produce spurious lines offset from the real one and that are called ghosts. Rowland ghosts result from large-scale periodic errors, on the scales of millimeters. They are located symmetrically around the real line, spaced from it according to the period of the error and with intensity that increases with the amplitude of the error. Lyman ghosts are farther from the real line and result from periodic errors on smaller scales, just a few times the groove spacing. Satellite lines are close to the real one and arise from a small number of randomly misplaced grooves The relative intensity of some forms of ghosts grows fairly rapidly with increasing order of the real line, so although they are unimportant in low-order instruments they may be significant with high-order echelle gratings.

Here is a ghost with a volume phase holographic gratinsg

Scattered Light Spectrometers are also subject to scattered light. Unlike imagers, where the twodimensional character of the data allows removing scattered light as a natural process during data reduction, spectrometers are basically one-dimensional instruments and it can persist into the final reduced spectra and be difficult to identify. A spectrograph with significant scattered light in its spectra can give erroneous readings for fundamental properties such as equivalent widths of spectral lines; the scattered light will be removed from the lines and spread into a pseudocontinuum. Scattered light can be measured by putting a filter into the beam that blocks all light short (or long) of some wavelength and then measuring any residual spectrum in the blocked range.

Schematic diagrams of three types of IFU:

Processing spectrometer data Carry out standard image reduction steps Dark and flatfield frames require extra attention because of 1.) the low signal levels; and 2.) the effects of the slit Assuming you have dithered the image along the slit, difference the images at two dither positions Removes sky, dark current (but still need dark for flatfield) Combine the two spectra

Trace the spectrum to allow fitting any distortions in its shape along the dispersion direction Extract it, and extract similar signals along sky ; if necessary, subtract sky from the spectrum (if the first differencing worked well this may not be needed) Apply the flatfield frame (after subtracting the dark) Put the reference star spectrum through the same steps Divide the target spectrum by the reference star spectrum Do a wavelength fit to a calibration lamp exposure (or in the NIR, the OH lines from the sky) Use the fit to adjust the wavelengths in the observed spectrum Multiply by a template spectrum of the reference star

If the slit and instrument transmission functions are well-known, the resulting spectrum can be used for line ratios (where all the relevant lines appear in a single spectrum) Often, though, we want to flux calibrate the spectrum. Rough values can be obtained with care using the spectrometer as if it did photometry However, slit losses are usually variable It can be better to obtain an image and use it to normalize synthetic photometry obtained from the spectrum This approach can be critical to getting calibrated results on an extended object.

Fabry Perot Spectrometers The Fabry Perot spectrometer obtains spectral information by dividing the photons into two beams using partially reflecting mirrors, delaying one of these beams relative to the other, and then bringing them together to interfere. This device is based on two parallel plane plates with reflecting surfaces. At the surface to the right, a portion of the input beam is transmitted and a portion reflected, and the reflected portion is again partially transmitted and reflected at the left surface. However, interference modifies this simple picture. If the spacing, l, causes a 180 o phase shift between the incoming ray and R 1, then there will be no light escaping to the left. Under this condition, the phase shift at T 2 will be 360 o and the interference at T 2 will be constructive, so the light will escape there. As the spacing between the surfaces is changed, the amount of light escaping to the right will be changed as varying amounts of constructive interference occur at the right side reflective surface.

Now consider the reflection and transmission between two such surfaces. The amplitude for the emerging light is the sum of the contributions of each emerging ray: where is the phase difference imposed by the reflections, where n is the refractive index of the material between the reflecting surfaces. (17)... ' ' ' ' 4 6 2 4 2 i i i i e r att e r att e r att att Ae (18) cos 4 d n We get the emerging intensity (see notes): R = r 2 is the reflected intensity. (20) cos 2 sin ) (1 4 1 2 sin ) (1 4 1 cos 2 1 ) (1 ) ( 1 ) (1 2 2 0 2 2 2 2 0 4 2 2 2 0 4 2 2 2 2 d n R R I r r I r r r I r e e r r a I i i out

Equation (20) shows that I out has maxima when m 2d ncos (21) where m is the order. It is also apparent that the these maxima are narrower in spectral range the closer R is to 1 (the closer the reflectivity of the surfaces is to being complete). The finesse of the device is R 1 R (22) (valid for R > 0.5). The spectral resolution to full width at half power of the transmission profile is R res m (23) and the free spectral range between transmission orders is the finesse times.

Transfer functions for plate reflectivities of 0.1, 0.42, 0.75, and 0.91; high reflectivities increase the finesse of the interferometer

Much of the performance of a Fabry Perot depends on the flatness of the plates and the quality of the coatings on them. Because of the many reflections, the plates need to be very flat. It is difficult to make coatings that have flat, high reflection over more than an octave of the spectrum. The tunable filter for JWST had a creative solution with plates that work from about 1.5 to 2.8, and then from 3.2 to about 4.6mm. However, technical problems killed this instrument.

A perfectly aligned Fabry Perot makes a bulls eye of alternating constructive and destructive interference, resulting in transmission and blocking of light.

If we place a detector at the center of the bulls eye and scan the distance between the plates, the fringes move from the center outward (or inward) and the wavelengths of maximum transmission scan along the spectrum. The scanning can be by moving one plate relative to another, or (for a solid FP), by tilting. It most be done very precisely to maintain parallelism.

As the finesse is increased, e.g. by using high reflectivity plate coatings, the Fabry Perot fringes become sharper

The transmission bands can be made sharper and particularly the blocking between them can be made stronger by multiple passes. These figures show the effect of a single pass and three passes. To the left, finesse = 50; to the right, finesse = 500.

To eliminate unwanted orders, it is common to use two Fabry Perot interferometers in tandem

This is what a Fabry Perot looks like:

Layout of the Fabry Perot spectrometer for SALT This instrument provides imaging spectroscopy over a 3 field and at spectral resolution from 2500 to 250,000.

As we go to longer wavelengths, the scale of a high resolution grating spectrometer goes as the wavelength. Here is TEXES, R = 100,000 at 10 microns.

It is based on an extreme angle echelle grating, 36 inches long.

Here are some of the grading specifications: 0.3 inch groove spacing (0.131 grooves / mm) 0.03 inch groove height 84.3 degree angle of incidence

This technology is clearly not going to scale well to 100 microns, or even worse to 1mm! (Remember that the throughput must go up with the wavelength as well as the grating length, so grating width and the diameter of the optics also must scale) An alternative to get high resolution is a Fabry Perot with plate reflectivity close to 1 (high finesse).

Here is a sub- and mm-wave spectrometer that uses a Fabry Perot for high resolution and a grating to separate its orders. FIBRE is being built for use on SOFIA. It provides spectral resolution of about 1200 within a cube about 8 inches on a side. The same resolution would require a huge grating spectrometer.

Interference filters are basically stacks of solid Fabry Perot spectrometers. Each one is called a cavity.

Stacking cavities gives a high level of blocking and sharp onsets of the transmission band.

Filter wavelengths change with tilt (and weakly with temperature). n o is the refractive index outside the filter and n e is the effective index in the filter.

The relation between the transform and the spectrum is not intuitively obvious.

Because the scan must be stopped at some path length, the spectral lines (after transformation) have feet. They can be suppressed by apodizing the transform, systematically reducing its high frequencies. The compromise is that the spectral resolution is reduced.

The SPIRE imaging Fourier Transform Spectrometer

End of Spectroscopy