Spectral range
Wavelength range
Approximate wavelength range of the spectrometer is required to properly initialize the calibration parameters. The approximate wavelength of the first and las pixel in the spectrum should be available from the user manual or specifications of the spectrometer. The wavelengths that are currently assigned to the individual data points/pixels are also typically stored alongside the acquired spectrum. Note that some CCD and CMOS detector-based spectrometers do not utilize the full range of sensor pixels. The wavelength range should include only the pixels that are read out of the detector array and are part of the acquired spectrum.
Calibration source
Gas-discharge calibration sources
This calibration tool readily provides a list of emission lines for several gas-discharge sources that can be conveniently used to calibrate spectrometers. The emission lines of such sources can be considered monochromatic. The main challenge with using gas-discharge lamps for calibration of spectrometers comes from the distribution of emission lines that can be too dense to resolve individually by spectrometers with a moderate resolution. Consequently, the positions of individual emission lines cannot be accurately derived by using simple methods, such as the center of gravity (COG). A similar issue arises, if the resolution of the spectrometer is sufficient but the number of data points in the spectrum that are related to a particular emission line is too small to accurately derive the position. This calibration tool overcomes the outlined limitations by modeling the full response of the spectrometer that includes all the relevant emission lines in the spectral range.
Supported standard gas-discharge sources
Calibration will initially include all the emission lines of the selected source that fall within the wavelength range of the spectrometer. The subset of emission lines can be further reduced during the interactive initialization process. An excellent source of information about emission lines is the Atomic Spectra Database of the National Institute of Standards and Technology.
Using a custom calibration source
If none of the listed sources fit your project, a custom set of spectral lines can be uploaded as a plain text or a CSV file.- Uploading a text file
If uploading a text file, make sure to set the file extension to .txt. The emission wavelengths must be given in units of nanometers using dot "." as decimal separator (not comma ","). List one emission wavelength per file line. The following example shows the content of a .txt file that includes the wavelengths of 10 emission lines.
- Uploading a CSV file
If uploading a CSV file, make sure to set the file extension to .csv. The first line of the file must include the column name "wavelength". The emission wavelengths must be given in units of nanometers using dot "." as decimal separator (not comma ","). List one emission wavelength per file line. The following example shows the content of a .csv file that includes the wavelengths of 10 emission lines.
Calibration spectrum
Improving the quality of calibration spectrum by averaging
The intensities of emission lines produced by gas-discharge sources can be spread over several orders of magnitude. Consequently the responses of weaker emission lines will be likely buried in the noise. This issue can be alleviated by taking the average of multiple spectra that should be all acquired using the same spectrometer settings (exposure time, gain and sensor temperature). The obtained average spectrum will exhibit a noise level that approximately drops with the square root of the number of averaged spectra.
Preparing calibration spectrum for upload
The calibration spectrum can be uploaded as a plain text or a CSV file.- Uploading calibration spectrum as a text file
If uploading a text file, make sure to set the file extension to .txt. List the spectrum intensities one per file line and use dot "." as decimal separator (not comma ","). The following example shows a section from the beginning of file spectrum.txt.
- Uploading calibration spectrum as a CSV file
If uploading a CSV file, make sure to set the file extension to .csv. The first line of the file must include the column name "intensity". List the spectrum intensities one per file line and use dot "." as decimal separator (not comma ","). The following example shows a section from the beginning of file spectrum.csv.
Uploading existing calibration for improved initialization
An existing calibration file that lists the wavelengths of each data point in the spectrum can be optionally uploaded to improve the initialization of calibration parameters. The existing calibration can be uploaded as a a plain text or a CSV file. A CSV calibration file can be downloaded as part of the calibration report.
- Uploading existing calibration as a text file
If uploading a text file, make sure to set the file extension to .txt. List the wavelengths one per file line and use dot "." as decimal separator (not comma ","). The following example shows a section from the beginning of calibration file calibration.txt.
- Uploading existing calibration as a CSV file
If uploading a CSV file, make sure to set the file extension to .csv. The first line of the file must include the column name "wavelength". List the spectrum intensities one per file line and use dot "." as decimal separator (not comma ","). The following example shows a section from the beginning of calibration file calibration.csv.
Point spread function model
Point spread function
Point spread function (PSF) is the response of spectrometer to a monochromatic or nearly monochromatic light such as emitted by laser sources. It holds fundamental information about the resolution of the spectrometer, which is frequently defined as the width of the PSF at half of the maximum intensity termed as the Full Width at Half Maximum (FWHM) resolution.
If two monochromatic sources emit light at wavelengths that differ by more than one FWHM, the emission lines can be resolved by the spectrometer.
On the other hand, if the emission wavelengths are less than 1 FWHM apart, the two sources cannot be resolved by the spectrometer.
FWHM of the PSF can change with the wavelength of light. This dependence is modeled by a polynomial function of selected degree. A good starting point should be a linear (order 1) polynomial model.
Point spread functions of spectrometers can take various shapes. This calibration tool offers four different parametric models of the PSF that well match the unique features of various spectrometers. These parametric models follow the Gaussian, Voigt, Sinc-squared and Triangular function.
Gausian, Sinc-squared and Triangular PSF models offer a single parameter that is uniquely related to the FWHM of the PSF. Consequently, a single polynomial is used to describe the wavelength dependence of the PSF. In contrast, the Voigt PSF model has two parameters which allows additional diversity of PSF shapes at any given value of FWHM. The additional flexibility comes at the cost of increased computational complexity, since two polynomials are required to model the wavelength dependence of the two PSF parameters. Both parameters are modeled by a polynomial of the selected degree.
The shape of the PSF can vary across different spectrometer types. A good starting point for diffraction-grating spectrometers should be the Gaussian and Voigt PSF models. Acousto-Optic Tunable Filter-based (AOTF) spectrometers will likely better work with the Sinc-squared PSF model.
Calibration model
Tuning curve
The mapping of data point locations/pixels from the acquired spectrum to wavelengths is accomplished by the tuning curve. A polynomial model is used to describe the mapping. For most spectrometers, a polynomial of order from 3 to 5 should be sufficient. Note that the maximum order of the tuning curve polynomial is limited to one less than the number of emission lines of the calibration source that are within the spectral range of the calibrated spectrometer. For robust estimation of the tuning curve polynomial coefficients, the emission lines should be spread across the full spectral range and exceed the minimum required number by a significant margin. Having wide spectral regions with no emission lines, in particular at the two ends of the range will likely increase the calibration error.
Baseline
Due to a number of different reasons, such at the dark current of the sensor, stray light and fluorescence, the acquired spectrum can contain a baseline signal. The baseline can be constant (offset) or slowly changing across the spectrum. A significant part of the baseline can be usually removed by subtracting the dark response of the spectrometer. However, if this is not possible or the baseline remains significant, the calibration will use a polynomial model to capture and fully remove the baseline. A low-order polynomial (1 - linear or 2 - quadratic) will in most cases be enough to remove the baseline.
