Beamsplitter efficiency

Figure 20-29 Fourier transform infrared spectrum of polystyrene film. The Fourier transform of the background interferogram gives a spectrum determined by the source intensity, beamsplitter efficiency, detector response, and absorption by traces of H20 and C02 in the atmosphere. The sample compartment is purged with dry N2 to reduce the levels of H20 and C02. The transform of the sample interferogram is a measure of all the instrumental factors, plus absorption by the sample. The transmission spectrum is obtained by dividing the sample transform by the background transform.

In summary, the amplitude of the interferogram as observed after detection and amplification is proportional not only to the intensity of the source but also to the beamsplitter efficiency, detector response, and amplifier characteristics. Of these factors, only 7(vo) varies from one measurement to the next for a given system configuration, while all the other factors remain constant. Therefore, Eq. 2.4 may be modified by a single wavenumber-dependent correction factor, 7/(vo), so that the ac signal, 5(8) (in volts), from the amplifier is... 

The performance of the beamsplitter is of vital importance to the successful operation of most FT-IR spectrometers and we consider the design and performance of beamsplitters in this section. Consider a beam of monochromatic radiation at wavenumber, V, entering a two-beam interferometer. Let the intensity of the radiation be 7(v) and let the reflectance and transmittance of the beamsplitter be and TV, respectively. For a beamsplitter that absorbs no radiation, Ry- -T = 1. As mentioned in Section 2.2, an ideal beamsplitter is one for which R and TV are equal to 0.5 across the entire spectrum that is measured. Usually, however, either R or TV is slightly greater than 0.5, which has the effect of reducing the beamsplitter efficiency. 

Figure 5.32. Variation of the beamsplitter efficiency, ART, with reflectance, R, assuming that the beamsplitter does not absorb any of the incident radiation. Provided that 0.28

The beamsplitter efficiency, r (v), is defined as 4RyTy. The variation of r (v) with Ry for a nonabsorbing beamsplitter is shown in Figure 5.32. It can be seen that ri(v) is equal to unity (100%) when Ry = Ty = 0.5, which was the case for the ideal beamsplitter discussed in Section 2.2. Provided that 0.28 < Rv < 0.72, the beamsplitter efficiency exceeds 80%. The practical achievement of efficiencies this high across the entire spectral range is one of the major accomplishments of beamsplitter manufacturers. 

Let us first consider self-supporting thin-film (pellicle) beamsplitters of thickness d. Chamberlain et al. [45] have shown that the beamsplitter efficiencies for parallel and perpendicular polarized radiation are given by... 

The relative beamsplitter efficiency of a film for unpolarized incident radiation is simply given by the average of the values for parallel and perpendicular polarized radiation ... 

Figure 5.34. Variation of RT (= n) with wavenumber, v or a, normalized to the center wavenumber, vo or ao, for a sihcon film n = 3.6) on a calcium fluoride substrate (w2 = 1.4) with a Cap2 compensator plate of the same thickness, with 0 = 45°, calculated for the first hoop of the beamsplitter efficiency curve. (Originally reproduced from [46], by permission of the author.)...

A good description of all the factors contributing to the efficiency of an FT-IR spectrometer has been reported by Mattson [10]. He measured the effect of several different parameters that include beamsplitter efficiency, Fresnel losses at the substrate and compensator plate, reflection losses at the mirrors, radiation obscured by the mounting hardware for the HeNe laser, the emissivity of the source, and losses caused by imperfect optical alignment. He calculated the overall efficiency ( in Eq. 7.8) as being 0.096. This value is in accord with the value of 0.10 used in Section 7.1 to estimate the SNR of a commercial FT-IR spectrometer. 

The values of dg p and dg for a sample with a refractive index of 1.5 are given for ZnSe and Ge in Table 15.3. As a first approximation for ATR spectra measured on a FT-IR spectrometer, the effective depth of penetration is simply the average of dgp and dg g. It should be recognized, however, that the beamsplitter efficiency is different for p- and i-polarized radiation, so again, this average is just an approximation of the true value of dg. It should also be noted that Eqs. 15 and 16 are only accurate for weak absorption bands because of the effect of anomalous dispersion. 

Any interferometer that is capable of at least 2-cm resolution at the excitation wavelength (1064 nm) can be used for FT-Raman measurements. Thus just about every interferometer that is sold today could be used for this pmpose. Because the throughput should be optimized, however, it is better to use an interferometer with a 4- or 5-cm-diameter beamsplitter than a smaller size. Since NIR Raman measurements with a Nd YAG laser are made between about 9300 and 6000 cm , the optimal beamsplitter should be one with a quartz substrate. While Cap2 and extended-range KBr beamsplitters have been used for FT-Raman spectrometry, it is usually advisable to purchase a beamsplitter that has been optimized for these measurements, as the higher the beamsplitter efficiency, the higher will be the signal-to-noise ratio of the spectrum. 

In the same way that variations in somce intensity, beamsplitter efficiency, and detector response are compensated in transmission spectrometry by ratioing the single-beam spectra measured with and without the sample in the beam, in PA spectrometry the single-beam spectrum of the sample is ratioed against the spectrum of an optically opaque and thermally thick reference. As noted above, carbon black and heavily carbon-filled polymers make excellent reference materials for PA spectrometry. 

Fig. 5.6.4 Reflectivity (solid curve) and beamsplitter efficiency (dashed curve) of a 10 /xm thick sheet of Mylar operated at 45° and 30°. Both planes of polarization are shown for both cases.

Under such circumstances the same instrument might be used to measure both VCD and ROA, albeit with different detectors and beamsplitters. So, even though there are numerous differences between the instrumentation for VCD and ROA measurements, both are very efficient in their own right and the future may bring opportunities for these two forms of VOA to borrow instrumental advantages from one another. 

In Eq. (3.3) T is transmission, equal to the fraction of light within the Ad and Qd monitored by the spectrometer that reaches the detector. It consists of at least two factors, the transmission of the collection and focusing optics and the transmission within the spectrometer itself. The transmission of the collection optics incorporates any losses from reflection of lenses, mirrors, or a sample cell, while the transmission of the spectrometer incorporates grating efficiency, mirror reflectivity, beamsplitter losses, and the like. In addition, T includes losses from optical filters that may be used between the collection optics and the spectrometer Q [Eq. (3.3)] is the quantum efficiency (c photon ), the fraction of photons reaching the detector producing an electron, which is subsequently counted. 

Both dispersive and nondispersive spectrometers can exhibit preferential transmission of light depending on its polarization. The efficiency of diffraction gratings and the polarization sensitivity of the beamsplitter can cause errors in the observed depolarization ratio, depending on several variables such as experimental geometry and Raman shift region. For this reason, it is often important to place a polarization scrambler between the sample and any polarization-sensitive components of the spectrometer other than the polarization analyzer itself. In addition, it is good practice to measure p for a few known systems to verify accuracy of the apparatus. 

Bruker IFS 114 are marked in Fig. 50. For the sample compartment (A 3), the reflection attachment (A 3a) is shown in Fig. 50 which can be inserted at one of the two foci. Characteristic and outstanding is the design of the Michelson interferometer in this instrument (A 2 in Fig. 50). The radiation emitted by the source is not collimated at first but focussed on the beam-splitter. The angle of incidence on the beam-splitter is rather small (nearly normal incidence). This is advant-tageous with respect to the polarization properties of the beam-splitter. We recall from Section 4.1 and Fig. 15 that the efficiency (4 RT) of thin film beamsplitters depends on its thickness, on its refractive index, on the wave number of the radiation, and, last but not least, on the polarization of the light. The latter dependence is rather drastic for angles of incidence near 45° which are close to... 

The cracial parts of the system are the polychromator and the transfer optics. Polychromators and monochromators are usually optimised for high spectral resolution. This requires keeping the optical aberrations on the path through the polychromator smaller than the slit width. The result is a relatively low f-number, typically 1 3.5 to 1 8. The f-number limits the fraction of the fluorescence light that can be transferred into the entrance slit (see Sect. 7.2.4, page 279). Moreover, the efficiency of any grating is far less than 100%. Therefore some loss of photons on the way from the sample to the detector in unavoidable. A multiwavelength system based on a polychromator is less efficient than a system based on dichroic beamsplitters, but by far more efficient than a system that scans the spectrum by a monochromator. 

Attenuator "A" attenuates the laser-beam power to the appropriate level which is allowed by the MCT detector (<0,5 mW). The optical signal scattered back from the target is collected by the same telescope that was transmittin the laser beam. This weak optical signal is introduced into the laser by the same mirrors and the same "S" beamsplitter, that were used in the transmission process. Inside the laser cavity this low intensity radiation is amplified in the same cavity mode in which the laser is operating. For this reason the mode of the received radiation is identical with local beam mode. This identity secures the best mixiflg efficiency for the heterodyne detection. This mode identity is the reason that we called our system self aligning The lens in front of the detector serves to fit the spot size of the local and amplified (received) beams to the detector size. 

---