Spectroscopy with a Rainbow Optics Spectroscope Al Brockman, Darwin NT, Australia 2004

In this article, I first describe the theoretical function of a spectroscope and the variety of types that have been constructed. I then show how to construct and use a simple spectroscope to record the spectral lines of some of the brighter stars and establish the spectral types of the observed stars.

Contents

• Introduction • Part I. Background • Principles of Spectroscopy • Types of spectroscopes • Part II. Observations of stellar spectra • Equipment used • Grating efficiency • Spectrum scale • Selection of stellar objects • Characteristics of the spectral classes • Observations • Image processing and data analysis • Sources of error and limitations • Conclusion • References

Introduction

“We know what the stars are made of, know of their structures and their lives, only because we are able to observe and analyze their spectra. Unbroken starlight allows us to admire a star's external characteristics; its spectrum allows us to look into its very soul”. James Kaler, 1998

These words by Kaler go the very heart of the importance of spectroscopy as being fundamental to our knowledge and understanding of our stellar (and quasi-stellar) universe.

Spectrography is one of the key disciplines of astronomy, perhaps even the most significant. Indeed, the essence of our physical knowledge of the stars comes from the spectral analysis of light which we collect with our telescopes.

Part I. Background

Principles of Spectroscopy

To produce a spectrum the light must be dispersed from a source and separated into its component colours. This can be done in two ways. The original method was to use a glass prism (see Figure 1) where the shorter-wavelength components of the incoming white light are refracted more both upon entry and exit, and are consequently bent through a greater angle than the longer wavelengths.

Red MIXED Violet

Red Violet

Figure 1. The dispersion of light by a prism. Incoming white light is dispersed by refraction into red and violet components, with all the other colours in between. The beam of white light is wide, and the colours produced by the individual rays overlap. The colour discrimination can be greatly improved by restricting the width of the incoming beam with a small aperture or slit.

The second way is to use a grating, which employs the principle of diffraction. If the wavelength of light is much smaller than the aperture or slit width, a light wave simply travels onward in a straight line after passing through, as it would if no aperture were present. However, when the wavelength exceeds the size of the slit, diffraction of the light occurs, causing the formation of a diffraction pattern consisting of a bright central portion (the primary maximum), bounded on either side by a series of secondary maxima separated by dark regions (minima; see Figure 2). The maxima and minima are created by interference of diffracted light waves. Each successive bright band becomes less intense proceeding outward, away from the central maximum. The width of the central bright portion, and the spacing of the accompanying sidebands, depends on the size of the aperture (slit) and the wavelength of the light. This relationship can be described mathematically and demonstrates that the width of the central maximum decreases with decreasing wavelength and increasing aperture width, but can never be reduced to the size of a point light source.

Figure 2. Intensity Distribution of Diffracted Light. From Molecular Expressions Microscopy: Light and Colour – Diffraction of light.

Practical Spectrographs To be practical for the amateur, a spectrograph must be reasonably simple to construct, reasonably robust in operation, and reasonably inexpensive. Four designs may fulfil these broad criteria: objective prism, grating-prism (grism), imaging slit, and fibre fed. The Objective Prism Spectrograph Perhaps the easiest way to create a spectrum is by placing a prism in front of a telescope. The light is dispersed even before it enters the telescope, which then brings the dispersed light to focus as a spectrum. They are used by professional astronomers to survey and catalogue large numbers of stars rapidly, since every star in the image appears as a spectrum. Disadvantages are that the prism must be approximately as large as the telescope objective, made of high quality glass, and polished accurately flat on both faces, making them extremely expensive. In addition, the incoming light is not linearly dispersed resulting in the distances between the various constituent wavelengths not being equal. Finally, starlight is superimposed on the full intensity of the night sky making it difficult to obtain the spectra of faint objects. The Grating-Prism Spectrograph The grism is probably the most practical way for an amateur to get into spectroscopy. It is a transmission grating combined with a prism. The grism is placed in the beam of light converging toward focus, usually a matter of centimetres ahead of focus. The grating disperses the light into a spectrum. The prism refracts the beam so that the spectrum

is formed directly behind the grism and corrects some of the optical aberrations introduced by the grating. The grism optical element is both small and relatively inexpensive (several hundred dollars) and are suitable for reflectors, refractors, and catadioptric telescopes. In addition, it is possible to shift the grism in and out of the converging beam without disturbing the optical configuration. Because of aberrations introduced by a grating, the zero-order image and the spectrum do not lie at exactly the same focus. Therefore, one must focus on the spectrum rather than on the zero-order image. Further details of grism design and the correction of aberration are followed up in Part II. The Slit Spectrograph This is an instrument designed to isolate a narrow strip of light from the focus of a telescope by means of a slit, pass it from the slit through a dispersing element, and re-image a wavelength-dispersed image of the slit on a detector. The two-dimensional spectrum recorded by the detector consists of a thin slice of sky in one axis and a sequence of images of the slit at different wavelengths spread along the other axis. These require sophisticated design and the spectrograph must form sharp images of the slit at different wavelengths over a wide range of angles with little or no vignetting. To avoid aberration by dispersing a converging or diverging beam, rays passing through the dispersing element must be parallel. The basic element of a slitless spectrograph are thus a slit to isolate a thin strip of light, a collimator to render the beam parallel, the dispersing element, and camera optics to re-image the slit in monochromatic light. The assembled spectrograph must be mounted solidly at the focus of a telescope, with adequate provision for focussing, viewing the location of the slit, and guiding. These present significant challenges to the amateur but some commercially available slitless spectrographs are available, most notably from the Santa Barbara Instrument Group (SBIG). The Fibre-Fed Spectrograph Because most professional high-resolution slit spectrographs were so bulky to mount at the focus of even large telescopes, thin optical fibres to carry light from the focus of the telescope to the slit of the spectrograph were developed in the late 1980’s (Berry & Burnell, 2000). By using hundreds of fibres at the focus of a telescope, massive surveys of galactic redshifts became feasible to the professional astronomer. For amateurs, fibre-fed designs move the spectrograph and CCD camera system to a convenient position beside the telescope. At the focus of a telescope is a “light pipe” to pick up starlight. This consists of a bundle of tiny optical fibres that conveys the starlight to the spectrograph. At the pick-up end, the fibres are bundled into a circular region to capture the whole star image, but at the output end, they are lined up side by side to form a narrow slit pattern.

The properties of the fibre bundle dictate the design. The spectrograph may employ a concave reflection grating to collimate, disperse, and focus the spectrum with just one optical element.

Fibre-fed spectrographs are compact and convenient but the background sky light must be digitally subtracted since starlight and background sky light are mixed into an image

as a single spectrum. The most popular commercially available fibre-fed spectrograph is undoubtedly the one produced by SBIG but costs many thousands of dollars. Part II. Observations of stellar spectra

In this section, a technique will be described and some observations presented for the acquisition of stellar spectra using a (relatively) low cost spectrograph. Equipment used My set up and optical image train consists of a 0.25 m (10”) f/10 Schmidt-Cassegrain telescope, motorized secondary focuser (Optec TCF-s), f/6.3 focal reducer, prism wedge and diffraction grating in a grating mount, and a CCD camera (SBIG ST-8) or a DSLR camera (Canon EOS 10D) as shown in Figure 3. Telescope

The optical tube assembly is a MEADE 0.25 m f/10 Schmidt-Cassegrain telescope on a German Equatorial Mount (Paramount ME, SW Bisque) which is supported on an Advanced Telescope Systems (ATS) portable pier. The telescope is permanently installed in a 3.5 m domed observatory (Sirius Observatories).

Figure 3. Optical system used for this project consisting of a 10” f/10 SCT operating at f/6.3 with a focal reducer. A SBIG ST-8 CCD camera is shown attached in this image.

Detector

The camera used for the majority of stellar spectra was a DSLR Canon EOS 10D. It is a low noise 22.7 x 15.1 mm CMOS sensor with an effective resolution of 6.3 megapixels (3,072 x 2,048), each 7.3 microns square. The sensor has the same 3:2 aspect ratio as 35 mm film but is smaller by a factor of 1.6. It has a built-in infrared blocking filter which cuts away the deep-red end of the visible spectrum and contributes to the camera’s poor red response, especially at the hydrogen-alpha (Hα) emission at 656.3 nm. Spectroscope

The grating used was a Rainbow Optics™ slitless blazed transmission grating having 200 lines per millimetre. It is suitable for stars but not extended objects since the entire field of view is used.

The prism is a 3º52’ wedge prism from Edmund Scientific. The 25 millimetres diameter prism fitted into the barrel of the Rainbow Optics grating in a grism arrangement as shown in Figure 4. The orientation of the prism relative to the grating grooves was critical. The deviation of the prism compensates the deviation of the grating at the cental wavelength. In addition, the grism arrangement was placed as close to the CCD as possible.

Figure 4. The 25 millimeter diameter wedge prism fitted into the Rainbow Optics barrel (grism configuration).

Grating Efficiency

The efficiency of a grating is a parameter which gives the percentage of energy concentrated in a given order and at a given wavelength. The closer this efficiency approaches 100% the better is the grating for the wavelength considered. Comparing a number of commercially available gratings, Christian Buil was able to determine that the Rainbow Optics grating gave the best efficiency by using a helium-neon laser and an Audine CCD camera as detector at a wavelength of 632.8 nm. Ignoring orders higher than 2 because of their weak contribution in general, Buil determined the relative efficiency at each corresponding order (see Table 2). Since most of the light is concentrated in the Ist order, the Rainbow Optics is a good quality grating.

Table 2. Rainbow Optics Grating efficiency

Order +2 Order +1 Order 0 Order -1 Order -2 0.7 % 67.6 % 22.5 % 6.6 % 2.6 %

Spectrum scale

In the plane of the CCD, the spectrum scale, expressed as Aº/mm (Angstroms per millimetre) and also known as the plate factor P, can be computed as:

710 .cos. .

Pk m d

β=

where, β is the angle of emergence after diffraction, k is an integer number for the spectrum order, m is the number of ruled grooves per millimetre, d is the distance between the grating and the focal plane.

For my system, if we assume that d = 21 mm and the first order (k = 1) is considered with m = 200 grooves/mm, then β = 3.7º for a wavelength of 0.65 um and the plate factor P = 2376 Aº /mm.

Since the CCD is sensitive between 4000 Aº and 9000 A, the linear extension of the spectrum is (9000 – 4000)/2376 = 2.10 mm. Since the CMOS chip in the Canon EOS 10D has pixels 7.3 um on a side, the spectrum length in pixels is 2.10/0.0073 = 288 pixels.

The pixel (ε) covers a spectral element whose size is:

dλ = ε.P

dλ = 9.10-3 . 2376 = 21.4 Aº. Selection of stellar objects

A list of bright stars that were currently visible in the sky at my location (Darwin NT, Australia 130º 50’ E, 12º 28’ S, -9.5 h GMT) over the period of observation (September – October 2004) was generated (see Table 2). The list includes stars from a number of the major spectral types (O, B, A, F, G, K and M).

Table 2. Eight Representative Bright Stars Observable from Darwin, NT, Australia Listed By Spectral Classification

Object ID Flamsteed-Bayer

Visual Mag

Spectral Class

Achernar α Eridani 0.50 B3Vp Alrescha α Piscium 3.82 A2 δ Sculptorus 4.59 AOV

Fomalhaut α Piscis Austrini 1.2 A3V

β Phoenicis 3.32 G8IIIvar Ankaa α Phoenicis 2.40 KOIII 57 Ceti ? M0/M1 IIIMaenkar 92 α Ceti 2.54 M2 III

Notes: 1. Spectral Classes are listed in O-B-A-F-G-K-M order (O being the hottest, and M the coolest). The Types (0-9) are gradations within the Class (0 hottest, and 9 coolest). 2. A hyphenated Spectroscopic Class designation indicates that the class of the star varies. 3. Luminosity Classes (I-V) indicate brightness and size (I- Most luminous supergiants. III – Giants. V – Main Sequence stars). An “a” or “b” indicates greater or lesser brightness within class.

Characteristics of the spectral classes

In the modern spectral sequence, OBAFGKMLT, the hydrogen absorption lines weaken in both directions away from class A.. Various other absorptions round out the picture. It was noted very early that the spectral sequence in this form correlates with colour, ranging from a blue tint for O and B stars to reddish for class M. Since colour depends on surface temperature, so must the spectral class, as shown in Table 3:

Table 3. The Spectral Sequence (from Kaler, 1998).

Class Spectrum Color Temperature

O ionized and neutral helium, weakened

hydrogen bluish above 31,000 K

B neutral helium, stronger hydrogen blue-white 9750-31,000 K

A strong hydrogen, ionized metals white 7100-9750 K

F weaker hydrogen, ionized metals yellowish

white 5950-7100 K

G still weaker hydrogen, ionized and neutral

metals yellowish 5250-5950 K

K weak hydrogen, neutral metals orange 3950-5250 K

M little or no hydrogen, neutral metals, molecules reddish 2000-3950 K

L no hydrogen, metallic hydrides, alkalai metals red-infrared 1500-2000 K

T methane bands infrared 1000 K

Observations

The observations were made with a grism spectrograph that combines a 25 mm diameter 3º 52’ prism wedge with a Rainbow Optics diffraction grating at the focal plane of the CCD camera. Images of the spectra were made with a Canon DSLR and digitally analysed using the freeware software Visual Spec (Spectrographic analysis software for astronomy).

Taking images of spectra was a challenge, but much easier than taking long guided exposures of deep sky objects since precise guiding was not an issue as star trailing in the right orientation assisted in making the spectrum wider and so help visualize the absorption lines.

First, the object to be imaged was centered on the CCD chip, and the scope's drive kept running. Using slow motions, the star was moved to one side of the chip which brings the first order spectrum into view on the chip. A quick 2-3 second integration of the star and its first order spectrum was made. Some time must then be spent on focus. Focus must be made on the spectrum, not the star, as the spectrum is created at a steep angle to the focal plane. Additionally, a sharp focus may only be achieved on one section of the spectrum at a time. For this reason, the placement of a small angle wedge prism in front of the diffraction grating had the desired effect of selectively refracting the incoming light so as to bring the entire spectrum into focus and thus counteract the chromatic aberration. Of course, the orientation of the prism wedge with the grating was critical to achieve the correct refraction to bring the entire spectrum into focus.

Once the star was focused, the CCD software was set to take a ten second integration. Once set, the mount's tracking power was turned off letting the star drift in R.A. Now the integration was activated. When complete, the drive was turned back on again.

The results will look something like the ten second integration of the star Alrescha (alpha Piscium) in Figure 5 taken through the 10” f/6.3 SCT and using the Canon EOS 10D. The reason for the slanted spectrum is that the grating was not aligned perfectly with the RA drift angle. By rotating the DSLR camera relative to the Rainbow Optics grating, better results can be achieved. Note the strong hydrogen lines in the blue part of the spectrum typical of a Class A spectral type.

Figure 5. Spectrum obtained of Alrescha (α Piscium) with the Rainbow Optics spectroscope.

Also, keeping the grating aligned with the CCD's pixel rows helps to keep things oriented better for these operations. Once aligned, the image looked more like the one of Sirius in Figure 6.

FOptics spectroscope and imaged with a SBIG ST8 CCD camera.

igure 6. Ist order spectrum obtained of Sirius (α Canis Majoris) with the Rainbow

Figure 7 Spectral images of seven stars representing some of the major spectral classes. Absorption lines and bands can be clearly seen for many of the stars from which spectral types can be ascertained by comparisons with sample spectra.

Things to note are the prominent lines in the blue end of the spectrum for the B, A and AO stars. These are likely to be hydrogen lines of the Balmer series. The G class star shows weaker hydrogen lines while the M class show no hydrogen lines and an abundance of metal lines in the green and red part of the spectrum. Proccessing and Data Analysis

For each star observed, it was intended that a spectral profile be made and the major lines identified. Due to the low noise of the CMOS sensor, dark frame subtraction was not necessary for the spectral images. Flat-fielding was also unnecessary but the images were rotated and cropped, levels adjusted in Adobe Photoshop CS and the files saved in fts format for importing into AIP4WIN. Six steps were required to extract the spectral curve from a star image obtained using the Rainbow Optics Spectroscope.

Step 1: Load the Spectrum Image. The image appears as a streak stretching across the middle of the display, with the wavelength increasing from left to right.

Step 2: Invoke the Spectroscopy Tool. Step 3. Select the region of the image containing the spectrum. These regions

include: • The background sky above the spectrum, • The region of the spectrum itself, and • The background sky below the spectrum.

The Spectroscopy Tool performs a median over the areas identified as sky background and subtracts them from the spectrum in order to remove the spectral contribution of the sky background from the stellar spectrum.

Step 4: Select the Spectrometer mode. Step 5: Select the Vertical Scale Type. There is the option of displaying the amplitude

on either a linear or logarithmic scale. Step 6: Generate the Spectral Curve and save the spectrum to file for importing into

Microsoft Excel. Once the spectral data had been loaded into a spreadsheet, the spectrum of a

calibration source taken with the same spectrograph can be similarly loaded. The wavelengths of the unknown spectrum are calibrated against a set of known spectral lines. Although I had a mini argon strip lamp, I was unsuccessful in my attempts to obtain a spectral image using the slitless spectrograph positioned at the focal plane of my telescope so consequently no calibrations were possible.

Figure 7. Spectrum obtained of Fomalhaut (α Piscis Austrinis) with the Rainbow Optics spectroscope and imaged with a SBIG ST8 CCD camera.

Spectral plot of Fomalhaut

1.00E+05

2.00E+05

3.00E+05

4.00E+05

5.00E+05

800 900 1000 1100 1200 1300 1400 1500

Pixel value

Inte

nsity

Figure 8. Spectral plot of Fomalhaut (spectral class A3V) showing intensity vs pixel value. Sources of error Errors related to the construction of the spectrograph

The main error, or aberrations, induced by this simple slitless star spectroscope is chromatic coma. It is dependent on the particular wavelength and its dimensions as a function of wavelength can be described mathematically. With chromatic coma, the resolution is independent of the grating’s groove number and the grating to focus distance as described in detail by Buil. It is possible to greatly improve the quality of the spectrograph by adding an optical component: a small angle prims with one side positioned against the grating. The prism completely cancels chromatic coma for a chosen wavelength λ0 as shown in Figure 8.

Figure 8. A prism is located

The deviation angle of the ally

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ch that incidence and diffraction angles are made equal. However, widening in a direction perpendicular to dispersion may cause a loss in detectivity and little benefit maygained.

Fut rather a cylindrical one. Since the CCD detector is flat, focus cannot be readily

achieved for every wavelength in the spectrum. For this reason, the order 0 image should be brought to sharp focus unless the CCD camera is given a slight angle with respect to the optical axis so that the plane of the detector intercepts at the same time the best focus position for order 0 and a given point of the spectrum.

The FWHM (Full Width at Half Maximum) dires spectrograph. Errors in tracking of the object should be minimized as much as

possible and the focus as sharp as possible. The telescope itself should be well collimatedobtain the best image. In addition, atmospheric turbulence is another factor to consider and times of steady seeing as well as imaging close to the object’s meridian are desirable. For all these reasons, it is easier to obtain good spectra with shorter focal length systems than with longer ones. E

g filter which cuts away the deep-red end of the visible spectrum and contributthe camera’s poor red response, especially at the hydrogen-alpha (Hα) emission at 656.3 nm. C telescope equipped with a grating spectrograph and a digital SLR or CCD camera can obtainspectral images of sufficiently good resolution to allow determination of their broad spectral classes. With suitable calibration spectra and freely available software, spectrograms can be created that can be used to define the actual wavelengths of the absorbed absorption an emission lines or bands. While this was not achieved by myself in this first instance, I willagain to get it right as time allows.

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