Fully Automated Wavelength Calibration Improves Accuracy of Spectroscopy

By AZoOptics

Table of Contents

Introduction
Motivation
     The Polonomial Fit Method
     Fit to the Czerny Turner Model
Basic Theory
Comparative Data
Major Implications
Appendix
About Princeton Instruments

Introduction

Along with the launch of a powerful LightField 64-bit data acquisition software by Princeton Instruments, a new completely automated wavelength calibration technique has been developed to attain unprecedented accuracy for spectroscopy applications a shown in Figures 1 to 4. The patent-pending IntelliCal technology is presently offered as a LightField package option and enables quick, consistent wavelength calibration with minimal user input. IntelliCal is a full-spectrum calibration routine that refines a theoretical spectrograph model based on the physical characteristics of the actual instrument being used. This technical note will initially provide a review of critical issues inherent to conventional calibration methods and then offer basic IntelliCal theory, comparative data, and major implications of the new method.

Motivation

The IntelliCal technology was developed mainly to overcome a number of limitations present in conventional wavelength calibration methods, particularly a large amount of dependence on user input for precision. Largely, the post-calibration wavelength precision is not used in the software programs used in these conventional methods, so determining this depends on the user.

By using a source that has several multiple known emission lines to light the entrance slit of the spectrograph, it is possible to determine a direct wavelength-to-detector pixel coordinate correlation.

Figure 1. IntelliCal source installed on an Acton Series SP2300 spectrograph from Princeton Instruments.

There are commonly two types of wavelength space calibration that include the following:

  1. A polynomial fit where only two or three emission lines are used
  2. A fit to the Czerny-Turner model.

The Polonomial Fit Method

Several routines utilize a polynomial fit to specify the spectral dispersion across the focal plane and thus acquire calibration results at the pixel level. This method, in which a polynomial is fit to a range of known emission lines, is both more precise and more difficult when compared to the other methods mentioned above. In this method, the user need not only determine which emission lines are seen by the detector, but they may need to redo the calibration every time the grating is moved. Also, the precision of this method is partially limited by the number of lines used to generate the fit; normally only two or three observed spectral emission lines are utilized.

Fit to the Czerny Turner Model

The wavelength space calibration is commonly used is a fit to the Czerny-Turner model. Here, the user is must choose a known emission line and the grating is moved so as to position the selected line at two or more locations across the CCD. The grating is then moved to another line. This process is repeated at least once. Next, the wavelength space residual is specified and minimized with respect to the standard Czerny-Turner model. The precision is correlated to n, which is the number of wavelength points used in the refinement.

Figure 2. Acton Series SP2500 spectrograph from Princeton Instruments with 1200 gr/mm grating and neon-argon USB lamp after IntelliCal routine.

Figure 3. Calibration error for an Acton Series SP2300 spectrograph from Princeton Instruments utilizing (a) IntelliCal and (b) standard routines. The relatively high RMS calibration error is due to the low dispersion of the grating used; much greater accuracies can be obtained with high-groove-density gratings.

Figure 4. Calibration error for an Acton Series LS785 spectrograph from Princeton Instruments utilizing (a) IntelliCal and (b) standard routines.

Basic Theory

IntelliCal is a completely automated calibration routine in which a non-linear least squares refinement algorithm is derived that minimizes the intensity space residual with respect to a theoretical model of the spectrograph. IntelliCal simulates the complete observed spectrum; the number of observables being always equal to the number of horizontal pixels in the CCD array. There is no need for any significant user input. The residual difference between observed and calculated emission line spectral intensities can be significantly reduced using Intellical.

This goal of reducing the difference is realized in three major steps that include the following:

  • Definition of an intensity function for a calculated spectrum.

  • Definition of the residual that will be minimized.

  • Definition of how the light is dispersed by the spectrograph.

    Czerny-Turner:

    Where:

Definitions

d = groove spacing
m = diffracting order
n = pixel numberx = pixel width
g = inclusion angle
f = focal length
d
= detector angle
s = spectral FWHM
l
’ = dispersed wavelength
y = grating angle

Comparative Data

Figures 5, 6, and 7 show the comparative calibration accuracy of IntelliCal with respect to conventional techniques. The comparisons are made in terms of wavelength error as a function of calibration line wavelength.

Figure 5. Wavelength error as a function of calibration line wavelength shows comparative calibration accuracy of IntelliCal versus Czerny-Turner model.

Focal length 500 mm
Aperture ratio f/6.5
Linear dispersion 1.52 nm/mm
CCD resolution 0.09 nm

Figure 6. Wavelength error as a function of calibration line wavelength shows comparative calibration accuracy of IntelliCal versus Czerny-Turner model.

Focal length 300 mm
Aperture ratio f/3.9
Linear dispersion 2.38 nm/mm
CCD resolution 0.14 nm

Figure 7. Wavelength error as a function of calibration line wavelength shows comparative calibration accuracy of IntelliCal versus polynomial fit (lens spectrograph).

Focal length 85 mm
Aperture ratio f/2
Linear dispersion 6.68 nm/mm
CCD resolution 0.20 nm

Major Implications

The benefits of the IntelliCal technology are listed below:

  • Intellical offers intelligent calibration. The software can recognize the instrument being calibrated.
  • User error is totally eliminated.
  • Every pixel in the detector is considered as an observable element, hence allowing IntelliCal to deliver tremendous gain in wavelength accuracy through highly over-determined refinement.
  • Spectra calibrated using IntelliCal can display up to a full order-of-magnitude improvement in wavelength accuracy when compared to traditional calibration routines.
  • Every observable emission line is utilized and spectral dispersion is refined at every pixel in the CCD array.
  • The observed spectrum is simulated to the pixel level; even doublets in a spectrum are accurately modeled and used in the calibration.
  • Each calculated spectrum displays the wavelength accuracy, quantitatively, at every pixel as shown in Figure 8. Also, the refinement is insensitive to line intensity.
  • Post-refinement capabilities are also highly impressive
  • Simulation of how any emission spectrum will appear at the detector for an arbitrary grating position, seamless combination with a pattern recognition algorithm, and searching all possible grating angles so as to fully determine the state of the instrument.
  • The most recent version of IntelliCal also provides intensity calibration, further improving the accuracy of recorded spectra.

Figure 8. IntelliCal has been designed to instill pixel-by-pixel confidence in data collected after calibration.

Appendix

IntelliCal offers highly accurate wavelength calibration quickly by following these simple steps:

  1. Install the IntelliCal source on the spectrograph. Alternatively, use the source to illuminate a fiber or place it at the sample position.
  2. Plug the source into the spectrograph’s USB port.
  3. Collect a background.
  4. Click “calibrate”.
  5. Either accept, or repeat to refine further.

About Princeton Instruments

Princeton Instruments designs and manufactures high performance CCD, ICCD, and EMCCD cameras; spectrographs; and optics-based solutions for the scientific research, industrial imaging, and OEM communities. We take pride in partnering with our customers to solve their most challenging problems in unique, innovative ways.

This information has been sourced, reviewed and adapted from materials provided by Princeton Instruments.

For more information on this source, please visit Princeton Instruments.

Date Added: Oct 28, 2011 | Updated: Jun 11, 2013
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