Spectral Response Correction: The Effect of Etaloning

Spectrometers are exceptionally versatile instruments capable of measuring light intensity in terms of its component wavelengths (i.e. by color). Fiber-coupled, cost-effective spectrometers like the IS Instruments MSP1000 (right) are used in different fields including agriculture, chemistry and biology, astronomy, lighting, etc.

A wide range of measurements need a variety of experimental setups, such as transmission, fluorescence, or reflectance/absorbance spectroscopy. The sensitivity to the system calibration can be critical based on the type of experiment.

For a wide range of spectroscopic applications, such as measuring relative spectral peak heights or carrying out absolute intensity or color measurements, it is essential to compensate for optical losses within the instrument. A relative correction, which creates a suitably shaped spectrum, should be performed for other applications. This article discusses how incoming light is affected by the spectrometer and what corrections can and should be performed.

Figure 1. (Left) A raw spectrum acquired of a tungsten halogen light bulb; (right) the same spectrum, corrected for instrument response

Figure 1 shows the raw spectrum observed by a given spectrometer along with the response when a correction algorithm is applied. The oscillating effect observed in Figure 1 exists in many compact spectrometers, and is because of etaloning within the instrument. The correction algorithm is considered to be a per-pixel intensity correction. The aim is to attain a scaling factor, for every single pixel on the CCD. These scaling factors correct for wavelength-dependent losses in the spectrometer. This is also known as a flat field in some disciplines, such as astronomy.

This indeed should not be confused with wavelength calibration, associating each pixel with a wavelength, which is most of the time provided by the manufacturer. The number of counts received by each pixel is adjusted by an instrument response correction. A few other processing steps like dark current subtraction are not wavelength dependent and should be routinely executed when a measurement is taken.

When Should I Correct for My Instrument?

For many applications, it is not necessary to correct for losses within the instrument even though the effect displayed in Figure 1 appears dramatic. For instance, this effect does not concern experiments that deal with relative measurements. This is the case in reflection or absorption spectroscopy. Since these measurements are carried out relative to a reference (for instance, the spectrum of an illuminated, empty cuvette), the effect of the instrument is canceled out.

It is not typically necessary to perform an instrument correction if one is looking for the presence of a characteristic spectral peak (or peaks), but not their relative heights. Wavelength calibration using a line-emission lamp is one such example.

However, it is important that the instrument response is accurately known and corrected if users want to perform a power measurement, a true color measurement, or a measurement of the relative heights of two peaks. A calibrated (for example NIST traceable) light source is needed for this process. A relative instrument correction is also possible if there is a light source with approximately known spectra, such as a common tungsten halogen light bulb.

Instrument Response

The instrument response is controlled by the performance of all the parts within the spectrometer. Mirrors and the detector in a spectrometer are not perfect and have differences across their surfaces due to manufacturing defects or dust. As light enters an optical system, it is absorbed and attenuated. This attenuation is wavelength-dependent, for instance a CCD has a wavelength sensitivity governed by its quantum efficiency (QE) curve.

Optical fibers and mirrors (Ag or Al coated) tend to have fairly low losses which are uniform across the (visible) spectral range of interest. The detector and grating can have more significant variations, as shown in Figure 3. Below 400 nm, standard fiber and mirror performance degrade considerably.

Figure 2. Left: Attenuation in a standard optical fiber. Right: Reflectance of unpolarised light incident on a silver coated mirror. The reflectance is above 96% for most of the visible region.

The QE of the detector and efficiency of the grating will have the largest contributing factor to the final signal for most systems. Gratings are optimized for a particular wavelength (or blazed). The efficiency curve for a typical grating, blazed at 500 nm is shown in Figure 3. Over a typical visible range of 400-850 nm, there is a difference of almost 30%. It is thus important to select a suitable grating for an application. IS Instruments supply spectrometers with different blaze angles ranging from 500 to 1000 nm to meet individual applications.

Figure 3. Left: Diffraction grating efficiency for a typical grating. Right: Spectral response of the Toshiba TCD1304AP/DG CCD sensor (adapted from manufacturer datasheet).

A silicon substrate is used for visible imaging detectors. Although silicon is well characterized, the actual form of the QE curve is different for every detector and a rough indication is typically provided in the manufacturer’s datasheet.

Interference from Detector Cover Glass

Detectors with cover glass are capable of producing an interference effect. This effect is commonly known as window etaloning. Incoming light undergoes multiple reflections between the cover glass and the surface of the detector, as well as within the glass itself, which leads to constructive and destructive interference. This is mainly pronounced in spectrometers because light incident on the detector is close to monochromatic. The effect is most obviously visible on broadband spectra as a low frequency oscillation or ripple in the signal.

Three reflection scenarios are possible (plus the base case when all the light is captured) for a detector with uncoated cover glass. These are shown in Figure 4. Novak et al., 1997 argue that the reflectance of the CCD could be low enough that the majority of the interference is caused only by the window. The effect is challenging to model numerically, hence it is difficult to find out exactly which reflection scenario is causing the problem. Peter Schlatter¹ carried out some interesting non peer-reviewed work investigating this phenomenon.

Figure 4. Reflections that occur inside a covered detector. The left image shows the usual case: light can reflect between the detector and glass. Middle: if a (double-sided) AR coating is used, most light that reflects off of the detector is lost. Right: If no cover glass is present, all the reflected light is lost.

The periodicity and exact shape of the signal is dependent on several factors, including the distance between the detector and the cover glass, as well as their reflectance.

A similar effect is observed in back-illuminated NIR detectors, where the detector substrate itself behaves as an optical etalon. Etaloning is an effect which takes place when light reflects between two flat surfaces, separated by a small distance comparable to the wavelength of the incident light. In back-thinned detectors, the optical thickness of the substrate is tens of microns which is 100 to 200 times the wavelength of the light. In the case of visible spectrometers, it is unlikely that true etaloning takes place because both the distance between the glass and detector and the cover glass thickness are much longer than a wavelength.

Removing Interference or ‘Etaloning’ Effects

A number of options are available for preventing this problem: it is first possible to apply an AR coating to both sides of the detector window. This retains the benefit of having a protective cover over the CCD, but may only decrease fringing rather than eliminating it. Secondly, the window can be completely removed. Finally, it is possible to use wedged cover glass. An optical wedge adjusts the refraction angle of light so that the outgoing and incoming rays are no longer parallel (and hence do not interfere). Figure 5 shows a comparison between windowless and window covered detectors used in IS-Instruments Mini spectrometers.

Figure 5. (Left) spectrum of a tungsten halogen lamp, using a window covered detector (MSP1000 spectrometer). Interference effects are clearly visible. (Right) spectrum of same lamp, using a windowless detector in the same spectrometer. No interference effects are present.

Using a windowless CCD is considered to be the most cost-effective and simplest solution. The disadvantage of this process is that removing the window exposes the detector to dust (after all, the purpose of the cover glass is mainly for protection). For spectrometers used in static environments, such as laboratories, this is unlikely to be a concern. If the spectrometer is used outdoors, moved frequently or even used in dusty environments, it may be an issue.

Most uses are advised to use a windowless detector for simplicity.

Correcting for Instrument Response

Full Radiometric Correction

The simplest way to compensate for the total spectral response of the system is to take the spectrum of a light source with a known emission. These lamps are available with calibration data and are capable of being used to perform radiometric correction of spectrometers. The procedure is basically the same as a relative amendment, but with an additional scaling factor. Additionally, a radiometric calibration is only applicable for the experimental setup where the rectification is carried out. For example, if a particular fiber is used to calibrate a spectrometer, changing the fiber would cancel the result. Even rotating the fiber should be avoided for some spectrometers.

There are other issues to be taken into account: a calibration lamp, before requiring a re-calibration, normally has a lifetime of less than 50 hours. Lamps need a warm-up period that can be up to half an hour, although obtaining the spectra may take milliseconds.

Calibration depends on accurate positioning of the lamp and other instrument geometries (such as the aperture size for the spectrometer), all of which adds some uncertainty.

For these reasons, manufacturers normally do not provide radiometrically calibrated spectrometers as standard. Yet, there are a few situations where this requirement is unavoidable.

Approximate Relative Correction

Approximation works reasonably well at removing instrument effects. A lamp with an emission spectrum close to a black body could be used – a common incandescent light bulb, for example. These lamps are made up of tungsten filaments and generate light by resistive heating. Their emission spectrum can be calculated using the Planck relation:

Where (ν, T) at frequency ν and temperature, c is the speed of light, h is Planck’s constant, and k is the Boltzmann constant. It is possible to use this equation to produce a theoretical blackbody spectrum for a lamp with a known temperature. The observed lamp spectrum is divided by this theoretical spectrum in order to give the relative instrument response. This response function is then used to multiply each new spectrum. Figure 6 shows an example response function. It must be noted that the scaling factor is considerably increased at higher pixel numbers, corresponding to longer wavelengths where the detector is less sensitive.

Figure 6. An example instrument response function generated using a household tungsten halogen lamp and a predicted blackbody spectrum. The sharp rise towards the right-hand side reflects that the CCD QE is poor in the infrared, so there is a larger correction here.

The correction of this issue is discussed at in detail by many authors ^[2]. It should be noted that within ^[2], the authors describe that the calculated emission spectrum for a halogen lamp, with a known color temperature, is shown to agree with the measured emission spectrum to within 5%. Since the accuracy of a traceable lamp is usually on the order of a few percent, this shows how accurate approximate corrections can be.

Conclusion

When carrying out spectral measurements, it is vital to understand what calibration steps are needed (if any). For relative measurements, it is not necessary to correct for the instrument response. Yet, if absolute measurements are needed then it is essential to perform either an approximate or full radiometric correction. If needed, IS Instruments can provide spectrometers with windowless detectors in order to avoid common interference effects.

References

¹ http://www.astrosurf.com/aras/fringing/schlatter/ripple.htm

[1] Novak, E., Ai, C., Wyant, J.C., 1997. Errors caused by nearly parallel optical elements in a laser Fizeau interferometer utilizing strictly coherent imaging. Proc. SPIE 3134, 456–460. doi:10.1117/12.295146

[2] Instrument Response Corrections, Technical Note 203, Horiba Jobin Yvon

This information has been sourced, reviewed and adapted from materials provided by IS-Instruments, Ltd.

For more information on this source, please visit IS-Instruments, Ltd.