Figure 1. A Hg spectrum emitted
by a MIDL® wavelength calibration lamp acquired by
Hyperspectral Imaging System. All wavelengths were acquired simultaneously in 10 ms.
Wavelength dispersion and spectral resolution
Spectral resolution is all about "separating" independent spectral emissions.
The easiest way to measure spectral resolution and wavelength accuracy is to acquire the spectrum of a standard wavelength calibration lamp. The spectrum shown in Figure 1 is that of a low pressure Hg lamp. The emission peaks appear at accurately known wavelength values and the spectral features have natural line widhtrsd of less that 0.01 nm.
Any broadening in the lines is, therefore, a measure of the instrument.
The spectral features in Figure 1 shows that all spectral features (peaks) below 650 nm are distinct and well separated, and above 650 nm, some lines are
merge together. The distinct lines are "resolved," the merged lines are not.
To calculate the spectral bandpass we only need to know two things: The slit width and average wavelength dispersion (AWD), measured in nm/mm, of the spectrometer.
If a spectrum is spread out over a long distance then features can be easily identified. Figure 2 shows the UV end of an Hg spectrum illustrating the ease with which each Hg line can be isolated.
High dispersion, a low value in nm/mm, the greater the potential for
high spectral resolution.
Low dispersion, a high value in nm/mm,
results in lower spectral resolution
Figure 2: Well separated, baseline resolved emission lines prove high resolution
Wavelength dispersion varies non-linearly with wavelength in both diffraction gratings and prisms. In the case of a diffraction grating linear AWD varies as the cosine of the diffracted angle, and in a prism as a function of refractive index.
In both cases iIf the detector pixels and slit width are matched then:
Bandpass = slit width x AWD (1)
If the slit is so narrow that no improvement in bandpass can be
then Bandpass = Resolution
How to estimate the average wavelength dispersion: For a wavelength dispersive hyperspectral imaging system that uses a CCD as the wavelength detector the easiest way to estimate the AWD is to take the total number of nm that cover one row of pixels and divide this by the length of a row. For example, the PARISS system present 365 to 800 nm over 8 mm or a spectral segment of 435 nm (800-365).
Therefore, the average wavelength dispersion =
435/8 = 54 nm/mm = AWD
A standard configuration of PARISS uses a 25 micron wide entrance slit:
Therefore: the average bandpass = FWHM = 54 x 0.025 = 1.35 nm.
In reality, because PARISS is prism based spectral resolution will be superior in the blue than in the red because the refractive index of glass is higher in the blue than in the red. Figure 2 shows that the spectral bandpass at the 405 nm line is 1 nm.
The influence of slit width on spectral resolution*
In a ideal world whenever a spectrometer records a spectrum it would perfectly reproduce the emitted spectrum. For example, if we recorded a laser emission through an ideal spectrometer there would be no detectable full width at half maximum (FWHM) we would observe a perfect "line". However, we are not in an ideal world, and this never happens!
All the spectra shown on this page were acquired on a PARISS® prism based Hyperspectral Imaging System.
Spectral resolution and bandpass depend on the width of the entrance slit aperture
Without exception all prism and diffraction grating based spectrometers image an entrance slit, at each wavelength, onto a detector - typically a CCD camera.
All wavelengths are captured simultaneously along all rows of pixels illuminated by the image of the entrance slit. Each pixel along a row corresponds to a particular wavelength.
If we know the number of pixels that correspond to the width of the image of the entrance slit we can determine the FWHM of an emission line.
The tools you need to determine spectral resolution:The easiest way to determine the relationship between pixel column and wavelength is to acquire a spectrum of a low pressure wavelength calibration lamp.
|"The slit width should be matched to the pixel size of the CCD camera for best spectral performance"
Researchers have two options: either use a pure low- pressure Hg lamp (WARNING! these lamps can damage eyes and skin) or an eye-safe multi-ion discharge lamp (MIDL) available through LightForm, Inc.
Figure 1 shows the spectrum of a pure Hg/Ar lamp in order to reveal the 365 nm line acquired on a PARISS system. (The dangerous 365nm line is dramatically cut by an MIDL lamp).
|Figure 3. Three camera pixels define the FWHM with a spectral resolution of
How to measure spectral resolution: Figure 3 illustrates the 404.7 nm Hg line acquired with the PARISS hyperspectral Imaging system.
Three CCD detector pixels define the FWHM for an observed resolution of 1 nm. The measured FWHM (in micron) corresponds to the width of the image of the entrance slit. (The pixel size is 9 micron corresponding to a slit width of 27 micron).
Key point: Ideally, the slit width should be matched to the pixel size of the CCD camera for optimum spectral performance.
In some applications, spatial resolution at the sample may point to working with a slit width that is not matched to pixel size.
This can be OK providing that the consequences are understood and acceptable.
Spectral Resolution = the FWHM of an Hg line when the using the narrowest possible slit width and smallest possible pixel size.
Bandpass = The FWHM when the slit width is greater than the narrowest width that would result in narrower lines.
Wavelength accuracy: Once the spectrum of an MIDL or Hg/Ar lamp has been acquired, the observed peak wavelengths can be compared to their actual wavelengths (to four decimal places) using wavelength tables published by the National Institute for Standards and Testing, or supplied with the lamp. Click here for an example covering the UV range shown in Figure 3.
Second order diffraction: Click here
*This web-page consists of extracts from the paper "Imaging Spectrometer Fundamentals for
Researchers in the Biosciences––A Tutorial" Jeremy Lerner, Cytometry Part A 69A:712–734 (2006) written by Jeremy Lerner (click here to request a copy of the PDF) or "The Optics of Spectroscopy a Tutorial".