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	Introduction		New page to record Spectroscopic observations   Spectroscopy Links: - Spectroscopy Ring  - Robin Leadbeater  - Dale Mais
	Star Analyser 100
	Spectral Lines - examples
	Spectral Lines - examples
	Dispersion, Plate Factor & Distance from grating to CCD
	Theoretical Resolution
	Practical Resolution
	Star Spectra Catalogue
	Star Spectra - Synthesized Colour
	Spectral Response of ST-7e CCD Camera (KAF-401-E)
	Spectral Response of UBVRI Photometric filters (Custom Scientific 1.25")

Introduction

Astronomical spectroscopy is the study is the spectrum of electromagnetic radiation, including visible , UV and infrared light which radiates from stars and other celestial objects. Spectroscopy can be used to derive many properties of distant stars and galaxies, such as their chemical composition and also their motion, via the Doppler shift.  

A bright hot source (like a star) emits a continuum of radiation which a spectroscope (diffraction grating or prism) can break down into a spectrum. When a light source passes through a tenuous gas consisting of elements, ions (plasma) or molecules, certain discrete wavelengths are removed from the continuum giving rise to dark absorption lines which fingerprint an element (and/or its ionic state) or molecule. The light from a star passing through the outer atmosphere layers of the star give rise to this effect. When a tenuous gas consisting of elements, ions and/or molecules is excited in some manner (collisional, electrically, heat or by light itself), the gas emits certain discrete wavelengths. These are seen as bright lines. Certain gaseous nebula or planetary nebula are good examples of this.

I began experimenting with spectroscopy in April 2008 soon after listening to an inspiring talk by Robin Leadbeater at a joint meeting of BAA VSS & AAVSO in Cambridge, 10-13th April, 2008. The talk was entitled 'Chasing Rainbows - The European amateur spectroscopy scene'. Covering both high-resolution and low-resolution spectroscopy, it included a description of what can be achieved with relatively simple slitless equipment incorporating Paton Hawksley's Star Analyser 100.

The Star Analyser 100 is a 100 lines/mm transmission grating set in a filter cell. It appeared that it could be relatively easily incorporated into my existing imaging set up, though I would have to free up one of the slots in my filter wheel used by one of my existing BRVI filters, and allow be to explore a whole new area of astronomical study.  Deciding that I could forego the use of my I-Band filter I quickly proceeded with the purchase of a Star Analyser 100 direct from the manufacturer and captured my first star spectra on 17th April 2008, just 6 days after hearing Robin's talk [ first spectra images, 2008-04-17].  

I typically work with Spectra dispersion of 33.5 A/pixel (3733 A/mm), and have a calculated practical resolution of between 70 and 110 A.

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Star Analyser 100

I began using a Star Analyser 100 in April 2008.

Star Analyser 100 - high quality transmission diffraction grating mounted in a standard 1.25 inch filter cell - high efficiency 100 lines/mm blazed design - grating surface protected by anti-reflection coated glass  - screws into an eyepiece or filter wheel like a normal filter  - star and spectrum can be recorded in the same image, which aids identification and calibration - provides low resolution slitless spectroscopy, but for relatively low cost (£78 + p&p, Apr 2008) Manufactured by : Paton Hawksley Education Ltd  Product Page :  http://www.patonhawksley.co.uk/staranalyser.html

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Star Spectra - examples

Vega,  blue-white star  A0 spectra

CCD Spectra Image 3 x 0.5s, 1x1 binning, Dispersion 33.6 A/px 2008-05-07 23:01hUT (#286046-48) (colour spectra is synthesized from black-white spectra)

R Aur, red star with infrared excess  M6-M8 spectra

CCD Spectra Image 5 x 60s, 1x1 binning, Dispersion 33.6 A/px 2008-04-24 22:05hUT (#284033-35) (colour spectra is synthesized from black-white spectra)

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Spectral Lines - examples

Spectral Absorption Lines in Vega (Lyra) O2 and H2O lines are due to absorption in the Earth's atmosphere) H-epsilon and H-zeta lines are not visible due to decreasing  sensitivity of CCD chip in violet region and overall low resolution.

CCD Spectra Image (200%) 3 x 0.5s, 1x1 binning,  Original Dispersion 33.6 A/px 2008-05-07 23:01hUT (#286046-48)

Spectral Absorption Lines in Deneb (Cygnus) O2 and H2O lines are due to absorption in the Earth's atmosphere)

CCD Spectra Image (200%) 5 x 5s, 1x1 binning,  Original Dispersion 33.6 A/px 2008-05-03 01:24hUT (#285161-65)

Spectral Emission Lines in P Cyg (Cygnus)

CCD Spectra Image (200%) 3 x 10s, 1x1 binning,  Original Dispersion 33.6 A/px 2008-05-08 01:16hUT (#286177-79)

Table of Balmer Lines

Transition of n →2 9→2 8→2 7→2 6→2 5→2 4→2 3→2 Name H-η H-ζ H-ε H-δ H-γ H-β H-α   eta zeta epsilon delta gamma beta  alpha Wavelength (A) 3646 3835 3889 3970 4102 4341 4861 6563

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Dispersion, Plate Factor & Distance from grating to CCD

Dispersion
Dispersion is a measure of the change in wavelength of the diffracted length along the surface of the CCD.  It is usually measured in angstrom per pixel.  It can be determined by observing a star spectrum that has known features.  For example in the following spectra of Vega, the H-alpha (6563 A) and H beta (4861 A) lines lie at original pixel values of 440 and 389 respectively.  

Dispersion  (image) = (6563 - 4861) / (440 - 389)    = 33.4 A per pixel

Based on several measurements of several pairs of lines in a number of spectral images an average dispersion value of 33.6 A / pixel was obtained.

Dispersion (average) = 33.6 A per pixel

Spectral Lines in Vega (Lyra)

CCD Spectra Image (200%) 3 x 0.5s, 1x1 binning,  Original Dispersion 33.6 A/px 2008-05-07 23:01hUT (#286046-48)

Plate Factor (P)
Plate Factor, P,  is similarly a measure of the change in wavelength of the diffracted length along the surface of the CCD, but is usually measured in angstrom per mm.   It can be determined from the above Dispersion value knowing the physical pixel size.

For my ST-7e camera (KAF-401-E),  the size of the pixels is 9 x 9 mm (0.009 x 0.009 mm)

Average Plate Factor, P = 33.6 / 0.009  = 3733 A / mm

Distance from grating to CCD (d)
It is not possible to accurately measure the distance between the grating and the CCD, however it can be calculated using the grating equation, which for slitless spectrography and first order spectrum reduces to  sin b = m l where b is the deviation angle, m is the number of grooves per millimeter and l is wavelength.

For Star Analyser 100 (100 groves/mm) I find that the H-alpha line (6563 A) typically lies at a distance of 196 pixels from the zero order star image. Thus, 

    x = 1.764mm  (from 196 * 0.009) 
    l =  0.0006563 mm 

    sin b = 100 g/mm * 0.0006563 mm 
    b = 3.7630 deg
    d = x / tan b  = 1.764 / tan (3.7630)  

    d = 26.82 mm

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Theoretical Resolution

A spectrograph's spectral resolution, R, determines the ability of the instrument to distinguish spectral features separated by Dl . The spectral resolution is a dimensionless quantity that is a measure of spectral purity (Dl).

For the case of my Meade LX200 8" (operating at f7.4), Star Analyser 100 and SBIG ST-7e CCD the following quantities are known: 

d = distance from grating to CCD = 26.8 mm 
k = order of spectrum = 1 
m = number of grooves per mm = 100 g/mm 
D = telescope diameter = 203.2 mm 
F = telescope focal length = 1498 mm 
N = F/D = focal ratio = 7.4

Since the entire surface of the grating is not illuminated the theoretical resolution becomes 

R = mLk, 

where L = gratings lit width (portion of grating illuminated by the star’s image from the telescope), or Dd/F

Dl =  l/ R

[ Reference: "Resolution Calculation for a Slitless Spectrograph" By Dr. Doug West. 
http://users.erols.com/njastro/faas/articles/west01.htm ]


For my setup  L = Dd / F = (203.2mm) x (26.8mm)/1498mm = 3.64 mm

The theoretical resolution, R  is thus given by  

R = (100 g/mm) x (3.64 mm) x (1) = 364

Spectrographs are considered low resolution when they have R<1000. This with an R value of just 364, my system is confirmed as being low resolution. 

My theoretical resolution, at H-alpha line (6563 A) is thus given by 

Dl =  l/ R = 6563 / 364 = 18 A

The actual resolution of the spectrograph (70 - 110 A) turns out to be much lower. 

With Dispersion of 33.6 A/pixel,  it is immediately apparent that the minimal resolution of the system has to be at least 67 A (from 2 x 33.6). Other factors limiting resolution are Chromatic Coma, Field Curvature and FWHM of the star image. 

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Practical Resolution

The actual resolution of a spectrograph turns out to be much lower than the theoretical resolution. Factors limiting resolution are Chromatic Coma, Field Curvature, FWHM of star image and Sampling Theorem (pixel size).  

For my setup FWHM and Pixel Size are the main limiting factors, which limit spectral resolution to a value of 70 A at best with a more typical value of around 110 A.

These values are derived from calculations shown below which are themselves based on equations given in 
"Resolution Calculation for a Slitless Spectrograph" by Dr. Doug West.  [http://users.erols.com/njastro/faas/articles/west01.htm].

1. Chromatic Coma
The practical formula for the effect of chromatic coma on spectural purity is 

Dl =  (3l)/ (16 N²),  where N is focal ratio

For my imaging system the effect of chromatic coma on spectural purity at the H-alpha line (6563 A) is 

Dl =  (3 x 6563 )/ (16 x (7.4)² )  = 22.5 A

2. Field Curvature
This is the effect on spectural purity cause by the aberration due to field curvature, which results from the cylindrical rather than planar nature of the spectrum’s focus. The defocusing effect produced by field curvature significantly reduces the spectrograph’s resolution.

Resolving power is given by

Dl =  DxP = PL ((1/cosb)-1)  

For my imaging setup at l= 6563 A,  b =  3.7630 deg, L = 3.64 mm and  P = 3733 A / mm, the spectral purity

Dl =  PL ((1/cosb)-1)  = (3733 A/mm) x (3.64mm) x ((1/cos3.763) -1) = 29.4 A

3. FWHM of Star Image

In a slitless spectrograph the full width at half maximum (FWHM) of the star’s image becomes the effective entrance slit width for the instrument. The larger the slit width the lower the resolution and spectral resolving power.

Dl =  (FWHM) x (e) x (P) / cos b

For my imaging setup at l= 6563 A,  b =  3.7630 deg, P = 3733 A / mm and typical FWHM of 4 arc sec, equivalent to 3.25 pixels at 1x1 binning, Dl becomes

Dl =  (3.25 px) x (0.009 mm)  x (3733) / cos 3.763  = 109 A

The spectral resolving power for other FWHM values is given in the table below.
In practice a FWHM of 2.0 and resolving power of 55 A is the best that can be achieved at my site for short exposures (1-2 secs duration).

FWHM (arc secs)		Dl
2.0		55 A
2.5		68 A
3.0		82 A
3.5		96 A
4.0		109 A
4.5		123 A
5.0		137 A
5.5		151 A

4. Sampling Theorem

When a continuous signal is sampled, such as a spectra, this process places a lower limit on the spectra purity. Simply put, the sampling theorem states that the highest frequency present in a sampled waveform is one half the sampling rate. The implication of this theorem on the spectrograph is that the smallest value of spectral purity possible is twice the wavelength interval covered by a pixel, or

Dl =  2 e P 

For my imaging setup with 9 mm (0.009 mm) pixels and P  = 3733 A / mm, smallest value of spectral purity is 

Dl =  2 e P = (2) x (0.009 mm) x (3733  A/mm) = 67.2 A

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Software Tools and Utilities

Image Acquisition

• Focusing Controller
  

Spectra Analysis

• Spectra Tab builder

• VSpec

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Star Spectra Catalogue

A catalogue of star spectra taken using LX200, Star Analyser 100 and SBIG ST-7e :

Star Name (designation)	Spectra Type (catalog)		Spectra Lines  ( Star Analyser 100)		Image Date/No. & Notes
SAO 49491 Cyg	WR Wolf Rayet				2008-04-18 (#283378-82)
SAO 69402 HD 190918, Cyg	Wolf Rayet				2008-04-25 (#284317-19)
Spica Alpha Vir	B1				2008-05-02 (#285031-35)
Regulus Alpha Leo	B7				2008-04-17 (#283073-75)
Albireo(B) Beta2 Cyg	B8				2008-04-18 (#283311-17)
4 Her	B9				2008-04-25 (#284120-22)
108 Vir	B9				2008-04-25 (#284301-05)
Vega Alpha Lyr	A0				2008-04-18 (#283304-10)
Vega Alpha Lyr	A0				2008-04-25 (#284127-31)
Deneb Alpha Cyg	A2				2008-05-03 (#285161-65)
Castor Alpha Gem	A2				2008-04-17 (#283070-72)
Procyon Alpha CMi	F5				2008-04-17 (#283058-60)
Izar Epsilon Boo	(A0)				2008-05-02 (285050-54)
Sadr Gamma Cyg	F8				2008-05-03 (#285149-53)
Groombridge 1830,  UMa	G8				2008-04-25 (#284161-63)
Pollux Beta Gem	K0				2008-04-17 (#283064-66)
Arcturus Alpha Boo	K2				2008-04-24 (#284006-9)
Albireo(A) Beta1 Cyg	K3				2008-04-18 (#283311-17)
61 Cyg	K5				2008-04-18 (#283268-70)
Betelgeuse Alpha Ori	M2				2008-04-20 (#283506-11)
Lalande 21185 HIP 54035, UMa	M2				2008-04-25 (#284178-80)
R Boo	M3-M8				2008-04-25 (#284310-12)
R Vir	M3-M8				2008-04-24 (#284089-91)
RR CrB	M5				2008-04-24 (#284052-56)
R Aur	M6-M9				2008-04-24 (#284033-35)
R Leo	M6-M9				2008-04-24 (#284043-45)
U Her	M6-M9				2008-04-17 (#283143-45)
P Cyg	B1Iapeq				2008-05-08 (#286177-79)
Y CVn	C5				2008-04-24 (#284106-10)
Cyg U	C7-C9				2008-04-25 (#284286-88)
NGC 6572 Pl. Neb	Pl. Neb				2008-04-18 (#283245-47)
NGC 6826 Pl. Neb	Pl. Neb				2008-04-18 (#283337-39)

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Star Spectra - Synthesized Colour 

Original monochromatic Spectral Displays with synthesized Coloured Spectral Equivalents The Synthetic Coloured Spectrums where generated by producing a coloured FITS image using the LRGB technique, in which the original monochromatic image was used for Luminance (L) frame whilst RGB frames where calculated from the calibrated wavelength profile. This calculation was performed via a software routine based on the Delphi Pascal 'WaveLengthToRGB' function listed on  efg's Spectra Lab page at http://www.efg2.com/Lab/ScienceAndEngineering/Spectra.htm  The 'original WaveLengthToRGB' function is based on Dan Bruton's work ( www.physics.sfasu.edu/astro/color.html  )
Visible Light Range
Star Name (designation)	Spectra Type (catalog)		Spectra Lines  ( Star Analyser 100) Monochromatic &  Approx Colour		Image Date/No. & Notes
Spica Alpha Vir	B1				2008-05-02 (#285031-35)
Spica Alpha Vir
Izar Epsilon Boo	A0 ??				2008-05-02 (285050-54)
Izar Epsilon Boo
R Aur	M6-M9				2008-04-24 (#284033-35)
R Aur					significant infrared component
NGC 6572 Pl. Neb	Pl. Neb				2008-04-18 (#283245-47)
NGC 6572 Pl. Neb

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Spectral Response of ST-7e CCD Camera (KAF-401-E)

From Kodak KAF-401 E performance specification (June 2000) (copy at http://www.lancs.ac.uk/depts/spc/resources/observatory/kaf-0401e.pdf )

Comparison of Spectra Response of ST-7e Camera,  with example stars.
Visible Light Range
CCD Camera Response (ST-7e )					Note relatively low  response at blue  end of spectrum, especially violet and UV
Spica Alpha Vir	B1				2008-05-02 (#285031-35)
Albireo(A) Beta1 Cyg	K3				2008-04-18 (#283311-17)
R Aur	M6-M9				2008-04-24 (#284033-35)
Star Name (designation)	Spectra Type (catalog)		Spectra Lines  ( Star Analyser 100) Monochromatic &  Approx Colour		Image Date/No. & Notes

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Spectral Response of UBVRI Photometric filters (Custom Scientific 1.25")

From http://www.sbig.com/products/filters.htm

Comparison of Spectra Response of ST-7e Camera,  UBVRI filter characteristics and example stars.
CCD Camera Response (ST-7e )					Note relatively low  response at blue  end of spectrum
Visible Light Range
UBVRI Filters
			Example stars
Spica Alpha Vir	B1				2008-05-02 (#285031-35)
Spica Alpha Vir					significant blue and  ?ultraviolet component
R Aur	M6-M9				2008-04-24 (#284033-35)
R Aur					significant infrared  component
Star Name (designation)	Spectra Type (catalog)		Spectra Lines  ( Star Analyser 100) Monochromatic &  Approx Colour		Image Date/No. & Notes

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