How reproducible a signal is, what is the smallest signal to be detected, what is the smallest change to be detected?
Signal change not caused by input change is unwanted. Each part of the optical chain is contributing.
Averaging is an appropriate means to improve signal quality. The improvement follows the square root law, e.g. an averaging of 100 gains an order of magnitude in signal quality. But any features related to drift cannot be approached by this.
Light source drift: a change in the emission – also in respect to the balance of the individual wavelength – is intrinsic to most light sources. During the warm-up period of some light sources such drifts occur on a time scale of about 30 minutes, until thermal equilibrium is reached. To make decent measurements this period should be skipped. Long term drift is caused by the material degradation of sources (filament burn off, UV glass solarization, material deposition on bulb surface). The only way to overcome such influence is to perform a light source monitoring, with a dedicate one spectrometer channel. Back to top▲
Light source fluctuation: this is the statistical contribution of light source uncertainties, caused by minor changes in operation current and other statistical process involved. Stable power supplies as well as spectra averaging helps to improve the signal quality. Back to top▲
Spectrograph variations derive mainly from drifts caused by thermal induced changes. These will lead to wavelength changes as well as to throughput and thus sensitivity (signal) changes. The choice of materials, design and mounting technology influence the significance. In case the drift behavior is predictable the influence might be corrected by software. Mechanical impact may cause changes too. In such cases, a complete recalibration of the spectrometer is required. Back to top▲
False light has two main contributions: straylight and second (higher) order contributions from the grating. While second-order blocking filters are a reasonable means to reduce the latter, there is no decent way to reduce straylight except to create components which causes little scattering. Beam stops help to prevent e.g. the zero-order light to hit the detector directly: The whole interior of a spectrograph is painted black to avoid any back-reflection from the walls. However, it is important to understand that most black paints have significant reflectivity in the NIR. Back to top▲
Readout noise is generated by the detector array and the operating electronics. It is typically independent from signal level, dominates at low signal levels / low illumination. Good electronics add only a few counts (at 16 bit).
Statistical (shot) noise: scales with the absolute signal generated in detector (array),
Noise = SQR(Signal) = Signal/Noise
E.g. at. 1M photoelectrons you have 1000 photoelectrons uncertainty (noise). At low signal e.g. 100 counts, the noise is 10 counts, still significantly higher than a few counts. If there is a significant dark current contribution, e.g. 1000 counts, we have more than 30 counts noise caused by that, limiting the low signal detection capability significantly. Back to top▲
S/N measured with Zeiss MCS spectrometer/tec5 electronics incl. Hamamatsu S3904 PDA and stabilized D2/Hal source
Signal-to-Noise is the ratio of the signal at a certain level to the noise at this level. If statistical noise is dominating above example gives S/N = 1M/1k = 1000. To achieve very high signal quality a detector array with a high well depth is required.
Dark current: varies with temperature change and integration time used. Controlling the temperature of a detector – best with an integrated thermo-electric cooler overcomes this problem. If the temperature changes are slow than a frequent renewal of the dark current measurement is an adequate means to compensate the influence too. The dark current measurement should be renewed after each change of integration time tInt.
To measure dark current the light source should be blocked. Only sources which reach thermal equilibrium fast may be shut off to do so. Systems with flash sources are easy, no flash during dark current measurements. Back to top▲
Linearity describes how good an optical signal is represented by the electronic data from the spectrometer electronics. Any deviation from a perfect linearity IEl = const x IOpt is mainly caused by the non-linear responsivity of the detector (array), while the contribution of the whole signal chain afterwards causes typically only little errors. As long as such deviations are stable they can be determined and then corrected by software. Most detectors have a deviation less than 1%. NMOS PDAs can have a deviation of various percent at high signal level, but still stable.
Quantifying a non-linearity starts with defining it, i.e. how to measure and analyze it. A convenient method is to use a very stable source (e.g. halogen), then vary the integration time of the detector array to change the signal level detected from almost zero to maximum. From the graph signal over integration time, a main slope (e.g. from the range between 25 to 50% of saturation level) can be used as reference against which any deviation is then calculated (e.g. as linearity error (LE) in % values). See also Detector Arrays. Back to top▲