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

This page summarizes chapter 8 of the book
"Fundamentals of Dispersive Optical Spectroscopy Systems",
ISBN 978081949824, SPIE monographs, Bellingham, WA, USA

Calibration of Spectrometers
 

This page presents the directory, the signs and symbols, conversions, and equations of the book, while the details are an exclusive part of  the book.

Pls Note: even the topic of Calibration is presented as part of the "Applications" here, it is part of the "Fundamentals" in the printed books.

Calibration, in optical spectroscopy, is separated into two applications:

C1-A - the calibration of the axis of dispersion / wavelength / photon energy
C1-B - the calibration of the axis of intensity / signal / illumination.

Part C1-B is also discussed in chapter 5 "Illumination / Radiometry".

C1-A - the calibration of the axis of dispersion / wavelength / photon energy
 

C1.1 Parameters to define the angular position of a dispersion element
The position of wavelength in a grating spectrometer depends mainly on:
the line frequency of the active grating, and
the working angle of the grating;
as calculated by equations  F1(1.1.0), F11 (2.2.1), and F12 (2.3.1) .
A prism spectrometer will output a certain wavelength as a function of the prism dispersion, which depends on the RI of the prism at the wavelength of interest, the angle of the prism, and the illumination angle, as calculated by F6 (1.4.6), F7 (2.16.6), and F9 (2.16.6).
But there are more parameters having impact on the actual wavelength output:
the internal angles of the spectrometer, which are implemented in F1, and F12,
and the actual temperature, which may change the wavelength, as described under F26 (2.15.1).
Furthermore the output position of a wavelength may change with the illumination of the entrance, and after vibration or shock where applied to the system. It should be kept in mind, that any modification in the beam travel inside the spectrometer may impact the calibration.
The consequence is, that the energy axis (wavelength, wavenumber, photon energy) needs at least to be checked frequently, and will need calibration in regular mode.
C1.2 How is a grating or prism spectrometer driven?
C1.2.1 Grating Spectrometers with sine functional drive
Graph C1-1 The sine Arm

Graph C1-1 is a combination of graph no17 and the behaviour of the sine function.
Graph C1-2:  the behaviour of angle and wavelength
Graph C1-2 demonstrates the relation between the working angle of a grating with 1200/mm and the sine and cosine.
C1.2.2 How to calibrate a scanning system with sinedrive?
C1.2.3 We start with the first calibration of a sine driven system.
Summary: a sinedrive actuated grating spectrometer only needs two calibration points.

C1.2.4
What parameters may deteriorate the linearity?
C1.2.5 When is recalibration or at least a check of calibration advised?
C1.2.6 What is required for a recalibration?
C1.3 Grating Spectrometers with rotary drive
Graph C1-3: Relations of position and wavelength,  disk driven
Graph C1-3 demonstrates the relation between the working angle of a grating with 1200/mm, mounted at a disk, and the angular function in comparison to a sine driven spectrometer.
C1.3.1 What is different at the first calibration of a disk system.
C1.3.2 What parameters may deteriorate the linearity?
C1.3.3 When is recalibration or at least a check of calibration advised?
C1.3.4 What is required for a recalibration?
C1.4 Calibration of the field output
According to the following equations is proven, that the dispersion, and therewith the distances between wavelengths slightly changes over the wavelength axis of the output field:
F1: m * l = k * (sin a sin b)
F3: m * dl = k * cos b * db 
or   db / dl  =  ( m / ( k * cos b ))
F18: f* (db / dl) = f * m / (k * cos b)
F19:  f = arcsin ( l /( 2 * k * cos e))
F20: RLD = (cos (x + f) * k) /( f * m)

Graph C1-4: the wavelength distribution in the ouput field
Graph C1-4 shows the wavelength distribution in the output plane of a spectrograph.
Additional parameters, important for area detectors:
C1.4.1 (see also 3.1.5) The output dispersion as function of the lateral position in the field output

 graph C1-5: the behaviour of dispersion in the output field

Graph C1-5 (= graph 58) displays four typical dispersion curves,
 

C1-B - the calibration of the axis of intensity / signal / illumination
 

C1.5 Introduction
Applications requiring a calibrated intensity axis, almost always deal with the portability of intensity data, without dependence on the system used for acquisition.
The common name for that kind of measurements is "Radiometry". It is described in the illumination chapter under 5.5, including the radiometric nomenclature and its equations. This chapter will deal with the practical aspects for reliable calibrations.
C1.5.1 Requirements for a useful calibration and portability of data
C1.5.2 Light sources for radiometric calibration
C1.5.3 Procedures
The curves involved, named by suggestion :
The original data:                                OD  in nW / nm 
Measured data from calib-source:    R     in A (the original output of the detector, can be different from current)
The instrument response:                   RC   from OD/R  in nW/(nm*A)
The unknown sample, DUT:               S      in A (dimension like R)
The final result:                                    SR   from S * RC  in  A*nW/(nm*A), the outcome is in nW/nm.

graph C1-6 the way to calibrate intensity
Graph C1-6
shows samples of curves involved in intensity calibration:
 

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