Optical Spectroscopy with dispersive Spectrometers
Basics - Building Blocks - Systems - Applications

Basics 2: Spectrometer Basics, Concepts, and Parameters

Please note: The content of the BASICS pages is available in printed shape since June 2014:

"Fundamentals of dispersive optical Spectroscopy Systems",
SPIE-Monograph, ISBN No.: 9780819498243

The internet pages have been reduced to the headlines, equations, and figures of the different chapters . We hope, that the brief collection and the complete and extended book will be as helpful and useful for you, as the spectra-magic.de/Basics have been.

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2.0.0 Fundamentals
Aim of the “Fundamentals” is to help starters with the definition and verification of the instrumentation for optical spectroscopy. Experienced spectroscopists and expert physicists will know some of the issues better and in deeper detail. But hopefully, every reader may find things worth mentioning. If any statement will be found not well explained or misleading, please write an e-mail to the address provided in the “Contact” page.

2.1.0 Introduction
It is the aim of “Basics“, to help the user with the justification of opto-spectroscopical instrumentation. The basics describe parameters and their association. Experienced spectroscopists and experts of the special physics will know details better and deeper, but hopefully, every reader may find useful information anyway.

2.1.1 The basic principle of a spectrometer
Graph 11 Basic Ray Travel
Graph 11, the components of a spectrometer for flexible use:

2.1.2 Attributes of modular spectrometers
Several basic spectrometer concepts exist, we look them up. 

2.2.1 The Littrow configuration

Graph 12 Littrow Top View
Graph 12, the Littrow mount seen from top
Graph 13 Littrow side view

Graph 13: Littrow configuration seen from the side and the front, having entrance and exit atop of each other.

2.2.2 Area correction by equation F13

2.2.3 Advantages and disadvantages of the Littrow

2.3.1 The Ebert-Fastie configuration
Angles and Definitions of the Ebert-Fastie

Graph 14, Ebert-Fastie setup seen from top

2.3.2 Ebert-Fastie area correction equation F14 :

2.3.2 Curved slits
2.4.0 The Czerny-Turner configuration
The Czerny-Turner spectrometer concept

Graph 15: The Czerny-Turner spectrometer and its angles The median angle at the grating of Ebert-Fastie- and Czerny-Turner-configurations

2.4.1 Imaging field corrections

2.4.6 The influence of the internal angles on the wavelength

2.5.1 Spectrometers for the Vacuum range 

Graph 16 Vacuum models
Graph 16: Spectrometer concepts for the Vacuum range 

2.5.2 Normal Incidence (NI)

2.5.3 Seya-Namioka

2.5.4 Grazing Incidence

2.6.1 Grating rotation and actuation

2.6.2 Direction of the grating rotation

2.6.3 The driving system
Graph 17: the sinedrive
Graph 17: The classical “sine-drive“

2.6.4 Grating position versus rotation

Graph 18 Triple Grating ratation
Graph 18: Influence of the grating rotation on the active surface

2.6.5 Grating actuation and steering are further described in Application C1.

2.7.0 Aperture and light flux (luminosity) 

2.7.1 Real Aperture or f-number?

2.7.2 Examples on the influence of the internal angles on the light flux

2.7.5 Comparing the calculations of f-number vs
W by light flux/luminosity
Comparison of Omega vs f-number
The illustration of f-number in comparison with
Graphically supported description of equation F17:
Graph L shows the origin of light flux calculation
Graph L: The luminosity at the spectrometer output by F17(new)

2.7.6 Monochromator examples

Spectrograph examples

2.8.1 The Dispersion
Gr 2A  Working Angles at the Grating
Graph 2A: the angles at the grating in a real spectrometer

2.9.1 Intensity distribution in the exit
Graph 19 Output distribution
Graph 19A. Intensity distribution in the exit / slit function
Graph 19B: spectral funtions at the exit slit
Graph 19B: Transfer Function and Distribution of the optical Power over the exit Slit.

2.10.1 Spectral resolution

Graph 20 Resoltuion by 50% criterion
Graph 20: Spectral resolution by the 50% criterion
Resolution at 10-%-Peak Ratio

Graph 21: Spectral resolution by the 50% rule, and peaks of different amplitude

2.10.2 Does one measure the resolution of the spectrometer, or that of the experiment?

2.10.3 When is a spectral curve completely reproduced?
SGraph 22 Gaussian peak fit
Graph 22: Situation of adjacent 22 or 23 data points to provide a Gaussian fit of a peak which is much wider then the bandwidth BW of the spectrometer.   

2.10.4 The Raleigh Diffraction Limit

2.10.5 Resolution of a monochromator compared to a spectrograph
Graph 23 Peak recursion in a mono
Graph 23: Peak reconstruction by a monochromator, if the line is finer than the instrument´s bandwidth, FWHM resolution is about 2.2 bandwidths
Graph 24 Peak recursion in a spectrograph
Graph 24: Peak reconstruction by a spectrograph, if the line is finer than the instrument´s bandwidth, FWHM resolution is at least 3 pixels = 3 bandwidths

2.10.6 Numerical resolution Rp  and Rr, and their wavelength dependence

2.10.7 A practical example on the optimization of resolution

2.10.8 Experimental examples on spectral resolution

Graph 25 4 real curvesdestortion
Graph 25: Typical resolution data, recorded by monochromators of different focal length. The darts in the graph refer to the notes in the description following

2.11.1 The image quality (Q-Factor or Fidelity)

2.11.2 What are the trouble makers in image transfer?

2.11.3 Aberrations
graph 26A_2 effects from spherical optics
Graph 26A the most common distortions (aberrations) in spectrometers with laterally opened angles
Graph 26 stigmatic and non stigmatic transfer
Graph 26B: Transfer function and stigmatic / astigmatic reproduction 

2.11.4 Astigmatism

2.11.5 Toroidal transfer systems

2.11.6 General aberrations and Coma
Graph 27 Origin of Coma
Graph 27: Coma effects
Graph 28 Coma disturbed spectrum
Graph 28: Example of spectral falsification from the Coma effect

2.12.1 False light, stray light, and contrast

2.12.4 The contrast ratio C, describing useful signal versus destructive signal
Graph29  Disturbance curves
Graph 29: Typical behaviour of the three main disturbances  

2.13.1 Double pass, Double and Triple spectrometers

2.13.2 The double pass spectrometer
Graph 30 Setup of double pass Ebert-Fastie
Graph 30: Beam configuration of a double pass spectrometer  

2.13.3 Double spectrometers

2.13.4 Subtractive spectrometers
Graph 31 Czerny-Turner double configuration
Graph 31: Typical double spectrometer setup, offering additive or subtractive operation  

2.14.1 Efficiency behaviour and analysis

2.14.2 Energy transmission and Bandwdith of single, double, and triple stage Spectrometers
Energy transmission and Bandwith of multiple stage monos

Graph 31A shows, how the energy transmission vs slit position changes with the number of stages

2.14.3 Effects of Photon travelling Time (Time of Flight)
Gr. 31B - Time of Flight Effects

Graph 31B describes the dispersion of travelling time, and the reduction of beam homogeneity, both versus the Aperture

2.15.1 Stability and thermal influence

2.15.2 Suggestions to minimize environmental influence
2.16.1 Reduction of unwanted spectral orders, and other filtering

2.16.2 Long pass filters
Graph 32 Edge filter curves
Graph 32: Typical order sorting filter curves (long pass filters) in the UV-Vis 

2.16.3 Bandpass filters and prism
Graph 33 Bandpass, short pass, prism curves
Graph 33 Typical transfer curves of bandpass filters, short pass filter, prism

2.16.4 Short pass filters

2.16.5 Echelle grating applications

2.16.6 The dispersion of a prism spectrometer

Graph 34 Prism dispersion
Graph 34: Reciprocal dispersion of a quartz prism with 30° angle, working in a spectrometer of 100 mm focal length.

2.17.1 Light transfer by optical fibres

2.18.1 General collection of performance parameters of spectrometers, and conclusion
Graph 35 Performance curve summary
Graph 35: Collection of the most important spectrometer parameters   

Hoping the study of the book Elements of dispersive optical Spectrometers will be of help for you, we remain with special thanks for your interest.

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