7/3/2023 0 Comments Limit of resolution calculatorPrevouisly, image enlargement through the spectrometer was reviewed. Bandpass (BP) is then given by:īP = FWHM ~ linear dispersion × (exit slit width or the image of the entrance slit, whichever is greater). (Aberrations may, however, still produce broadening of the base). If the two slits are perfectly matched and aberrations minimal compared to the effect of the slits, then the FWHM will be half the width at the base of the peak. From Figure 18, the FWHM, due to the slits, is determined by either the image of the entrance slit or the exit slit, whichever is greater. In general, most spectrometers are not routinely used at the limit of their resolution so the influence of the slits may dominate the line profile. In practice, the FWHM of F(λ) is determined by the convolution of the various causes of line broadening including:ĭλ (resolution): the limiting resolution of the spectrometer is governed by the limiting instrumental line profile and includes system aberrations and diffraction effects.ĭλ (slits): bandpass determined by finite spectrometer slit widths.ĭλ (line): natural line width of the spectral line used to measure the FWHM.Īssuming a Gaussian line profile (which is not the case), a reasonable approximation of the FWHM is provided by the relationship: The overall instrumental line profile P(λ) is related to the convolution of the individual terms:ĭetermination of the FWHM of the Instrumental Profile quality of the system's components and alignmentĮach of these factors may be characterized by a special function Pi(λ), each obtained by neglecting the other parameters.width of the exit slit or of one pixel in the case of a.The shape of the instrumental line profile is a function of various parameters: The recorded function F(λ) is the convolution of the real spectrum and the instrumental line profile. Let P(λ) be the instrumental line profile. Let F(λ) be the recorded spectrum through the spectrometer. Let B(λ) be the real spectrum of the source to be analyzed. Thus, there is a relationship between the instrumental line profile, the real spectrum and the recorded spectrum. The bandpass is then defined as the Full Width at Half Maximum (FWHM) of the trace, assuming monochromatic light.Īny spectral structure may be considered to be the sum of an infinity of single monochromatic lines at different wavelengths. The resultant trace will show intensity versus wavelength distribution.įor a monochromator, the same result would be achieved if a monochromatic light source is introduced into the system and the grating rotated. The output of the detector is recorded and displayed. For a given set of entrance and exit slit parameters, the grating is fixed at the proper orientation for the central wavelength of interest and the laser light source is scanned in wavelength. The instrumental profile may be determined in a fixed grating spectrograph configuration with the use of a reasonably monochromatic light source such as a single mode dye laser. The line profile now has finite width and is known as the “instrumental line profile” (instrumental bandpass) (Fig.26). In reality, spectrometers are not perfect and produce an apparent spectral broadening of the purely monochromatic wavelength. 24) which is a perfect line at precisely λ o. 23) and is analyzed by a perfect spectrometer, the output should be identical to the spectrum of the emission (Fig. If a light source emits a spectrum which consists of a single monochromatic wavelength λ o (Fig. This depends on many factors including the width of the grating, system aberrations, spatial resolution of the detector, and entrance and exit slit widths. In the most fundamental sense both bandpass and resolution are used as characterization of an instrument's ability to separate adjacent spectral lines.Īssuming a continuum light source, the bandpass (BP) of an instrument is the spectral interval that may be isolated. 24) which is a perfect line at precisely λo. If a light source emits a spectrum which consists of a single monochromatic wavelength λo (Fig.
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