EP4767036A1

EP4767036A1 - MEASURING DEVICE WITH FABRY-PEROT INTERFEROMETER

Info

Publication number: EP4767036A1
Application number: EP24790116.8A
Authority: EP
Inventors: Heikki Saari; Christer Holmlund
Original assignee: VTT Technical Research Centre of Finland
Current assignee: VTT Technical Research Centre of Finland
Priority date: 2023-10-12
Filing date: 2024-10-04
Publication date: 2026-07-01
Also published as: FI131821B1; WO2025078722A1; FI20236129A1

Abstract

An apparatus (500) for spectral measurements comprises: - a Fabry-Perot interferometer (FP1) having an adjustable mirror gap (dGAP), and - a control unit (CNT1) for controlling the mirror gap (dGAP), wherein the apparatus (500) is arranged to: - set the mirror gap (dGAP) to a first mirror gap value (dGAP,1) to provide a first spectral transmittance peak (P1,A) at a first wavelength (λA), wherein the first spectral transmittance peak (P1,A) has an effective spectral width (Δλ1,A,EFF), - change the mirror gap (dGAP) to a second different mirror gap value (dGAP,2) to provide a second spectral transmittance peak (P2,A) at the first wavelength (λA), and a third spectral transmittance peak (P1,C) at a second wavelength (λC), and - control the position of a mirror (M2) of the Fabry-Perot interferometer (FP1) near the second different mirror gap value (dGAP,2) such that the effective spectral width (Δλ2,A,EFF) of the second spectral transmittance peak (P2,A) is substantially equal to the effective spectral width (Δλ1,A,EFF) of the first spectral transmittance peak (P1,A).

Description

MEASURING APPARATUS COMPRISING A FABRY-PEROT INTERFEROMETER FIELD The present invention relates to a measuring apparatus, which comprises a Fabry-Perot interferometer. BACKGROUND A spectrometer may be implemented e.g. by using a tunable Fabry-Perot interferometer and a detector. The spectral measurement range of the Fabry- Perot interferometer is often intentionally limited so that the spectral measurement range comprises only one spectral transmittance peak. This typically facilitates spectral measurements, as the intensity of light transmitted through the Fabry-Perot interferometer to the detector may be directly associated with the single wavelength of said spectral transmittance peak. SUMMARY An object is to provide an apparatus, which comprises a Fabry-Perot interferometer. An object is to provide a method, which comprises using the Fabry-Perot interferometer. According to an aspect, there is provided an apparatus of claim 1. Further embodiments are defined in the other claims. The scope of protection sought for various embodiments of the invention is set out by the independent claims. The embodiments, if any, described in this specification that do not fall under the scope of the independent claims are to be interpreted as examples useful for understanding various embodiments of the invention. Fabry-Perot interferometer has two semi-transparent mirrors, which are substantially parallel with each other. The wavelength of a transmittance peak of the Fabry-Perot interferometer is inversely proportional to the effective distance between the mirrors. The effective distance is called herein as the mirror gap. The spectral transmittance peak may also be called as a passband. The mirror gap and the position of the transmittance peak are changed by using one or more actuators, which are controlled by a control unit. The method is discussed first by referring to a situation where the method comprises using the first order of interference and using the second order of interference. The method is subsequently generalized to a situation where the method comprises using a lower order of interference, and to using a higher order of interference. The mirror gap of a Fabry-Perot interferometer may be set to a first value to provide a first spectral transmittance peak of the first order of interference (m=1). The peak may be shifted to longer wavelengths by increasing the mirror gap. The Fabry-Perot interferometer may eventually have also a second spectral transmittance peak of the second order of interference (m=2) at a second mirror gap. The distance between the peak of the first order of interference and the peak of the second order of interference (at the same mirror gap) is called as the free spectral range (FSR). The Fabry-Perot interferometer may simultaneously have two or more spectral transmittance peaks, in a situation where the spectral measurement range is greater than the free spectral range, and the mirror gap is equal to the second mirror gap value. Thus, the Fabry-Perot interferometer may transmit light simultaneously at two different wavelengths, corresponding to the first order of interference (m=1) and to the second order of interference (m=2). However, the simultaneous presence of the two peaks may mean that the intensity of light transmitted through the Fabry-Perot interferometer cannot always be directly associated with only one wavelength. The present method may comprise providing a first spectral transmittance peak of the first order of interference (m=1) at the first mirror gap value, controlling the mirror gap of the Fabry-Perot interferometer so as to increase the effective spectral width of the spectral transmittance peak of the second order of interference (m=2), and using the first spectral transmittance peak to eliminate the second spectral transmittance peak of the second order of interference (m=2) at the second mirror gap value. The distance between the peak of a lower order of interference and the peak of the next higher order of interference is also called as the free spectral range (FSR). The Fabry-Perot interferometer may transmit light simultaneously at two different wavelengths, corresponding to the lower order of interference and to the higher order of interference. The present method may comprise providing a first spectral transmittance peak of a lower order of interference (m_L) at the first mirror gap value, controlling the mirror gap of the Fabry-Perot interferometer so as to increase the effective spectral width of the spectral transmittance peak of a higher order of interference (m_H), and using the first spectral transmittance peak to eliminate the second spectral transmittance peak of the higher order of interference (m_H) at the second mirror gap value. The symbol m_L denotes a positive integer. The m_H denotes a positive integer, which is greater than m_L. The difference m_H-m_L may be e.g. equal to 1, 2, or 3. The effective width of the second peak may be increased by controlling the gap between the mirrors such that the effective width of the second peak is substantially equal to the effective width of the first peak, so as to allow eliminating the second peak by subtracting the first peak from the second peak. The apparatus may comprise a detector to detect light, which is transmitted through the Fabry-Perot interferometer. The contribution of the second peak to the signal of the detector may be substantially eliminated if the effective width of the second peak is substantially equal to the effective width of the first peak. The effective width of the second peak may be increased e.g. by vibrating or tilting a mirror of the Fabry-Perot interferometer. The method may comprise: - setting the mirror gap (d_GAP) to a first mirror gap value (d_GAP,1) to provide a first spectral transmittance peak (P_1,A) at a first wavelength ( ^_A), wherein the first spectral transmittance peak (P_1,A) has an effective spectral width ( ^ ^_1,A,EFF), - changing the mirror gap (d_GAP) to a second different mirror gap value (d_GAP,2) to provide a second spectral transmittance peak (P_2,A) at the first wavelength ( ^_A), and a third spectral transmittance peak (P_1,C) at a second wavelength ( ^_C), and - controlling the position of a mirror (M2) of the Fabry-Perot interferometer (FP1) near the second mirror gap value (d_GAP,2) such that the effective spectral width ( ^ ^_2,A,EFF) of the second spectral transmittance peak (P_2,A) is substantially equal to the effective spectral width ( ^ ^_1,A,EFF) of the first spectral transmittance peak (P_1,A). The Fabry-Perot interferometer may have a first spectral transmittance function T₁( ^) in the situation where the mirror gap is equal to the first value, and the Fabry-Perot interferometer may have a second spectral transmittance function T₂( ^) in the situation where the mirror gap is near the second value. The term "near" includes the situation where mirror gap is equal to the second value. The contribution of the spectral transmittance peak of the second order of interference (m=2) may be substantially eliminated by calculating a linear combination of the first spectral transmittance function T₁( ^) and the second spectral transmittance function T₂( ^). In general, the contribution of the spectral transmittance peak of a higher order of interference (m_H) may be substantially eliminated by calculating a linear combination of the first spectral transmittance function T₁( ^) and the second spectral transmittance function T₂( ^). The method may provide an extended spectral measurement range for an apparatus, which comprises a Fabry-Perot interferometer, and/or the method may provide improved spectral resolution. The method may provide an extended spectral measurement range and/or improved spectral resolution for a spectral imaging apparatus, which comprises a Fabry-Perot interferometer and an image sensor. The spectral imaging device may be e.g. a hyperspectral imager. The method may provide an extended spectral measurement range and/or improved spectral resolution e.g. for a spectral imaging apparatus, which comprises a Fabry-Perot interferometer and a panchromatic image sensor. The panchromatic image sensor may provide improved spatial resolution e.g. when compared with an RGB image sensor, which comprises a Bayer filter. The method may comprise increasing the spectral width of a spectral transmittance peak of the Fabry-Perot interferometer. The spectrally broadened transmittance peak may subsequently be eliminated by linear combination of the spectral transmittance functions. Broadening and eliminating the spectral transmittance peak may enable increasing the spectral operating range of the Fabry-Perot interferometer. Broadening and eliminating the spectral transmittance peak may enable increasing the spectral operating range of a spectral imaging device, which comprises the Fabry-Perot interferometer. Broadening the spectral transmittance peak and subsequently eliminating the spectral transmittance peak may enable increasing spectral resolution of the Fabry-Perot interferometer. The method may further comprise modifying the spectral transmittance function of the Fabry-Perot interferometer so that the spectral width of the transmittance peak is constant over a predetermined spectral range. In other words, the spectral resolution may be arranged to be constant over a predetermined operational wavelength range of the Fabry-Perot interferometer. Broadening the spectral transmittance peak may also enable providing a tunable light source, which has a possibility to control spectral bandwidth of emitted narrowband illumination. The wavelength ^_PEAK of the maximum of a spectral transmittance peak P is: where d_GAP denotes the mirror gap, e.g. the effective distance between the mirrors of the Fabry-Perot Interferometer, and m denotes the order of interference. The free spectral range, i.e. the spectral separation ^ ^_FSR between a first peak of order m (at the wavelength ^_PEAK) and a second adjacent peak of higher order m+1 (at the wavelength ^_PEAK+ ^ ^_FSR) is: 2 ^ ^ _{^^ ^^ ^^} = ^{( ^ ^^ ^^ ^^ ^^)} 2_{∙ ^^∙ ^^ ^^ ^^ ^^} (1b) Using a higher order of interference m and/or using a greater mirror gap d_GAP may reduce the free spectral range so that an additional spectral transmittance peak appears in the spectral measurement range. However, the additional peak of the higher order may be eliminated by using a peak of a lower order. The spectral widths of the peaks may be equalized, and the peak of the lower order may be subtracted from the peak of the higher order. The spectral width of a spectral transmittance peak may be specified e.g. by the FWHM width ^ ^_FWHM, where FWHM means the full width at half maximum. The spectral width of a spectral transmittance peak is inversely proportional to the mirror gap d_GAP and inversely proportional to the order of interference m: 1 ^ ^ _{^^ ^^ ^^ ^^} ^ ^^∙ ^^ _{^^ ^^ ^^} (1c) Thus, using a higher order of interference m and/or using a greater mirror gap dGAP may improve spectral resolution. By broadening the spectral width of a peak of a higher order of interference, and by combining measurement results obtained with two different mirror gaps, it is possible to improve the spectral resolution and/or to extend the spectral measurement range of the Fabry-Perot interferometer. The effective spectral width of a spectral transmittance peak of the Fabry-Perot Interferometer may be increased by varying the mirror gap and/or by tilting the second mirror with respect to the first mirror. The effective spectral width of a spectral transmittance peak may be increased e.g. by adding a gap distribution modification signal to the drive voltage of the actuators of the Fabry-Perot Interferometer. The effective spectral width of a spectral transmittance peak of the Fabry-Perot Interferometer may be increased by controlling the mirror gap according to a sequence of mirror gap values. The mirror gap may be set according to the sequence. The actuators of the interferometer may be driven according to the sequence. The control of the mirror gap may be based on a list of air gap set values which are used as inputs to the control electronics in a sequence during an exposure time. The sequence may be a predetermined sequence. The sequence may be retrieved from a memory e.g. as lookup table. The mirror gap values may exhibit e.g. normal distribution, Weibull distribution, lognormal distribution, or random distribution. The sequence may also be generated in real time according to a suitable random number generator to provide a suitable distribution of mirror gap values. The use of three actuators may allow tilting the second mirror in several directions. In an embodiment, the three actuators may be driven with a phase difference of 120 ^ so that the normal of the second mirror may rotate about the optical axis of the interferometer. By using three different tilted mirror planes with different average mirror gap it is possible to modify the mirror gap distribution more accurately than when using only one tilted mirror plane. BRIEF DESCRIPTION OF THE DRAWINGS In the following examples, several variations will be described in more detail with reference to the appended drawings, in which Fig.1a shows, by way of example, a Fabry-Perot interferometer, Fig.1b shows, by way of example, a spectral measurement range, and a spectral transmittance function of the Fabry-Perot interferometer, Fig.1c shows, by way of example, a spectral measurement range, and a spectral transmittance function of the Fabry-Perot interferometer, Fig.2a shows, by way of example, a first spectral transmittance function of the Fabry-Perot interferometer at a first mirror gap, Fig.2b shows, by way of example, a second spectral transmittance function of the Fabry-Perot interferometer at a second mirror gap, Fig.2c shows, by way of example, the first spectral transmittance function and the second spectral transmittance function, Fig.2d shows, by way of example, the first spectral transmittance peak of the first spectral transmittance function at the first wavelength, and the second spectral transmittance peak of the second spectral transmittance function at the first wavelength, in a situation where the second spectral transmittance peak is not spectrally broadened, Fig.3a shows, by way of example, increasing the spectral width of the second spectral transmittance peak by varying the mirror gap, Fig.3b shows, by way of example, increasing the spectral width of the second spectral transmittance peak by tilting a mirror of the Fabry- Perot interferometer, Fig.4a shows, by way of example, the first spectral transmittance peak of the first spectral transmittance function at the first wavelength, and the second spectral transmittance peak of the second spectral transmittance function at the first wavelength, in a situation where the second spectral transmittance peak is spectrally broadened, Fig.4b shows, by way of example, temporal evolution of the mirror gap during the averaging time period, Fig.4c shows, by way of example, the probability density of mirror gap values during the averaging time period, Fig.5a shows, by way of example, the first spectral transmittance function, and the second spectral transmittance function, in a situation where the second spectral transmittance peak of the second spectral transmittance function is spectrally broadened, Fig.5b shows, by way of example, a modified spectral transmittance function, which is formed as a linear combination of the first spectral transmittance function, and the second spectral transmittance function, Fig.6 shows, by way of example, evolution of the mirror gap as a function of time, Fig.7a shows, by way of example, the spectral transmittance function at a first time, Fig.7b shows, by way of example, the spectral transmittance function at a second time, Fig.7c shows, by way of example, the spectral transmittance function at a third time, Fig.7d shows, by way of example, the spectral transmittance function at a fourth time, Fig.8a shows, by way of example, a modified spectral transmittance function formed as a linear combination of measured spectral transmittance functions, Fig.8b shows, by way of example, a modified spectral transmittance function formed as a linear combination of measured spectral transmittance functions, and Fig.9 shows, by way of example, method steps for eliminating a peak of a spectral transmittance function. Fig.10a shows, by way of example, scanning ranges for a Fabry-Perot interferometer, Fig.10b shows, by way of example, scanning ranges for a Fabry-Perot interferometer, Fig.10c shows, by way of example, scanning ranges for a Fabry-Perot interferometer, Fig.10d shows, by way of example, scanning ranges for a Fabry-Perot interferometer, Fig.11a shows, by way of example, in a three-dimensional view, a Fabry- Perot interferometer, which comprises three actuators, Fig.11b shows, by way of example, actuator driving units and distance monitoring units of a Fabry-Perot interferometer, Fig.11c shows, by way of example, in a three-dimensional view, tilting the second mirror of the Fabry-Perot interferometer, Fig.12a shows, by way of example, a spectrometer apparatus, which comprises a Fabry-Perot interferometer, Fig.12b shows, by way of example, a spectrometer apparatus, which comprises a tunable illuminating unit having a Fabry-Perot interferometer, Fig.12c shows, by way of example, a spectral imaging apparatus, which comprises a Fabry-Perot interferometer, and Fig.12d shows, by way of example, a spectral imaging apparatus, which comprises a tunable illuminating unit having a Fabry-Perot interferometer. DETAILED DESCRIPTION Referring to Fig.1a, the tunable Fabry-Perot interferometer FP1 comprises a first semi-transparent mirror M1, a second semi-transparent mirror M2, and one or more actuators ACU1 to adjust the effective distance d_GAP between the mirrors M1, M2. The effective distance d_GAP between the mirrors M1, M2 is called herein as the mirror gap. The first mirror M1 may be e.g. a stationary mirror, and the second mirror M2 may be e.g. a movable mirror. The Fabry-Perot interferometer FP1 may provide transmitted light B2 by filtering received input light B1. The mirrors M1 may comprise reflective dielectric layers and/or a reflective metal layer. The first mirror M1 has a first solid-gas interface surface SRF1. The second mirror M2 has a second solid-gas interface surface SRF2. The thickness d_M1, d_M2 of the semi-transparent mirrors M1, M2 is greater than zero. The thickness d_M1, d_M2 may be e.g. in the range of 10 nm to 50 nm. The effective distance d_GAP between the mirrors M1, M2 may be slightly greater than the distance between the interfaces SRF1, SRF2. The effective distance d_GAP may be defined e.g. by the equation 1a. Using a very small mirror gap d_GAP may involve a risk of accidental contact between the surfaces SRF1, SRF2 of the mirrors M1, M2. The contact may damage the mirrors M1, M2. The mirror gap d_GAP may be kept e.g. greater than 200 nm in order to reduce or avoid the risk of damaging the mirrors M1, M2. The semi-transparent mirrors M1, M2 may also be implemented as dielectric multilayer structures. The thickness of the mirrors M1, M2 may also be e.g. in the range of 500 nm to 1500 nm. The Fabry-Perot interferometer FP1 may be arranged to operate e.g. in a visible range of wavelengths and/or in an infrared range. The thickness of the mirrors M1, M2 may be e.g. in the range of 10 nm to 1500 nm. The input light B1 may be e.g. continuous light. The spectral intensity distribution I_B1( ^) of the input light B1 may be e.g. independent of time or substantially independent of time. The spectral intensity distribution I_B1( ^) of the input light B1 may remain the same or substantially the same during changing of the mirror gap. The spectral intensity distribution I_B1( ^) of the input light B1 may remain the same or substantially the same when the mirror gap is equal to a first mirror gap value, and also when the mirror gap is controlled in the vicinity of the second different mirror gap value. The mirror gap d_GAP may have a first mirror gap value d_GAP,1 at a first time t_A, and the mirror gap d_GAP may have a second mirror gap value d_GAP,2 at a time t_C. The spectral intensity distribution I_B1( ^) at the time t_A may be equal to or substantially equal to the spectral intensity distribution I_B1( ^) at the time t_C. Referring to Fig. 1b, the spectral transmittance function of the Fabry-Perot interferometer FP1 may comprise a first spectral transmittance peak P_2,A at a first wavelength ^_A, and a second spectral transmittance peak P_1,C at a second wavelength ^_C. The spectral distance ^ ^_FSR between the adjacent spectral transmittance peaks (P_1,C, P_2,A) is called the free spectral range (FSR) of the Fabry-Perot interferometer FP1. The free spectral range ^ ^_FSR is approximately equal to ( ^₀)²/(2 ^d_GAP). The spectral measurement range MSR1 of the Fabry-Perot interferometer FP1 has a lower limit ^_LP and an upper limit ^_SP. The measurement range MSR1 may simultaneously comprise two spectral transmittance peaks (P_1,C, P_2,A), in a situation where the measurement range MSR1 is greater than the free spectral range ^ ^_FSR. A spectral measurement may comprise measuring the intensity of the light B2 transmitted through the Fabry-Perot interferometer FP1. The simultaneous presence of the two peaks may make interpretation of the spectral measurement more difficult, because the transmitted light B2 may simultaneously have a first spectral component at the first wavelength ^_A, and a second spectral component at the second different wavelength ^_C. Referring to Fig.1c, the measurement range MSR1 may be reduced and/or the free spectral range ^ ^_FSR may be increased, so as to ensure that there can be at most one spectral transmittance peak in the measurement range MSR1. Referring to Fig.2a, the Fabry-Perot interferometer FP1 may have a first mirror gap d_GAP,1 at a first time t_A, so as to provide a first spectral transmittance function T₁( ^), which has a first spectral transmittance peak P_1,A at a first wavelength ^_A. The first mirror gap d_GAP,1 may be selected small enough, so as to ensure that there can be at most one spectral transmittance peak in the measurement range MSR1. The lower limit ^_LP and the upper limit ^_SP of the measurement range MSR1 may be defined e.g. by one or optical filters. The one or more filters may be arranged to provide a spectral transmittance function T_CUT( ^), for defining the measurement range MSR1. Referring to Fig. 2b, the Fabry-Perot interferometer FP1 may have a second mirror gap d_GAP,2 at a second time t_C, so as to provide a second spectral transmittance function T₂( ^), which has a second spectral transmittance peak P_2,A at the first wavelength ^_A. The second mirror gap d_GAP,2 may be greater than the a first mirror gap d_GAP,1, so that the second spectral transmittance function T₂( ^) may have a third spectral transmittance peak P_1,C at a second wavelength ^_C. The measurement range MSR1 may comprise two peaks P_2,A and P_1,C. The peak P_2,A may correspond to the second order of interference (m=2) at the wavelength ^_A, at the mirror gap d_GAP,2. The peak P_1,C may correspond to the first order of interference (m=1) at the wavelength ^_C, at the mirror gap d_GAP,2. Fig.2c shows the first peak P_1,A at the first wavelength ^_A, the second peak P_2,A at the first wavelength ^_A, and the third peak P_1,C at the wavelength ^_C. Referring to Fig. 2d, the first peak P_1,A corresponds to the first order of interference (m=1), and the second peak P_2,A corresponds to the second order of interference (m=2). The effective spectral width ^ ^_1,A of the first peak P_1,A at the first wavelength ^_A may be greater than the effective spectral width ^ ^_2,A of the second peak P_2,A at the first wavelength ^_A. The effective spectral width ^ ^_EFF means herein the difference ( ^_R,AVE- ^_L,AVE) between the average spectral position ( ^_R,AVE) of the first edge of a peak (P) and the average spectral position ( ^_L,AVE) of the second edge of said peak (P), wherein the spectral positions ( ^_R,AVE, ^_L,AVE) of the edges are determined at the half maximum height of said peak (P). The spectral positions ( ^_R,AVE, ^_L,AVE) of the edges may be averaged over an averaging time period ^t_AVE. The averaging time period ^t_AVE may be e.g. in the range of 100 ^s to 100 ms. The averaging time period ^t_AVE may be e.g. in the range of 1 ms to 100 ms. (1 ms = 0.001 s). The averaging time period ^t_AVE may be e.g. substantially equal to 100 ^s, 1 ms, 2 ms, 5 ms, 10 ms, 20 ms, 50 ms, or 100 ms. The mirror gap d_GAP may be varied e.g. in the range of d_GAP,AVE - ^d_VIB to d_GAP,AVE + ^d_VIB. d_GAP,AVE denotes the average mirror gap during the averaging time period ^t_AVE. ^d_VIB denotes the maximum deviation from the average mirror gap d_GAP,AVE during the averaging time period ^t_AVE. The maximum deviation ^d_VIB may be e.g. in the range of 5 nm to 50 nm. The maximum deviation ^d_VIB may be e.g. in the range of 0.5% to 10% of the average mirror gap value d_GAP,AVE. The maximum deviation ^d_VIB may be e.g. substantially equal to 20 nm. The position of the second mirror M2 with respect to the first mirror M1 may be varied near the average mirror gap value d_GAP,AVE (e.g. near the value d_GAP,2). The term "near" includes the situation where mirror gap is equal to the average value. For operation in the visible range, the mirror gap d_GAP may be varied e.g. by ^ 20 nm. The mirror gap d_GAP may be varied e.g in the range of d_GAP,2 -20 nm to d_GAP,2 +20 nm during the averaging time period ^t_AVE. For operation in the infrared range, the amplitude of the variation of the mirror gap may also be greater. For example, the mirror gap d_GAP may be varied e.g in the range of d_GAP,2 -200 nm to d_GAP,2 +200 nm during the averaging time period ^t_AVE. The effective spectral width ^ ^_EFF of the peak (P) is equal to the full width at half maximum width (FWHM) of said peak (P), in a situation where the mirror gap d_GAP is constant. The effective spectral width ^ ^_EFF of the peak (P) is greater than the full width at half maximum width (FWHM) of said peak (P), in a situation where the mirror gap d_GAP is varied. Referring to Fig. 3a, the effective spectral width ^ ^_EFF may be increased by varying the mirror gap d_GAP. The mirror gap d_GAP may be varied by moving the mirror M2 at non-constant velocity. The velocity of the mirror M2 may be accelerated and decelerated. The velocity of the mirror M2 may be accelerated and decelerated during the averaging time period, so as to provide the desired effective spectral width ^ ^_EFF. The second mirror M2 may be moved (SHAKE1) in the axial direction AX1 at non-constant velocity. The velocity of the second mirror M2 may be changed e.g. by more than 50% during the averaging time period ( ^t_AVE). In particular, the second mirror M2 may be moved back and forth during the averaging time period. The velocity of the second mirror M2 may be accelerated and decelerated during the averaging time period. The velocity of the second mirror M2 may be repetitively accelerated and decelerated during the averaging time period. The second mirror M2 may be vibrated in the axial direction AX1 (SHAKE1). For example, the second mirror M2 may be shaken. The second mirror M2 may be vibrated during scanning. The second mirror M2 may be vibrated in a situation where the average value of the mirror gap is changed. The average value of the mirror gap d_GAP may be changed e.g. according to a substantially linear function of time. The velocity of the second mirror M2 may be repetitively accelerated and decelerated several times during a scanning time period, wherein the average value of the mirror gap d_GAP is increased or decreased e.g. by 100 nm during said scanning time period. The velocity of the second mirror M2 may be reversed several times during a scanning time period, wherein the average value of the mirror gap d_GAP is increased or decreased e.g. by 100 nm during said scanning time period. Referring to Fig.3b, the effective spectral width ^ ^_EFF may also be increased e.g. by tilting the second mirror M2 with respect to the first mirror M1. The optical axis AX1 of the Fabry-Perot interferometer FP1 may be perpendicular to the first mirror M1. The surface normal N2 of the second mirror M2 may be tilted by a tilt angle ^₂ with respect to the optical axis AX1. In case of the tilted mirror M2, the mirror gap d_GAP,a at a first edge of the mirror M2 is slightly different from the mirror gap d_GAP,b at a second edge of the mirror M2. The method may comprise controlling the position of a mirror M2, with respect to the other mirror M1, by tilting the mirror M2, near an average mirror gap value d_GAP,AVE (e.g. d_GAP,2), so as to increase the effective spectral width ^ ^_EFF. Referring to Fig.4a, the mirror gap d_GAP may be varied and/or the mirror M2 may be tilted such that the effective spectral width ^ ^_2,A,EFF of the second peak P_2,A is equal to the effective spectral width ^ ^_1,A,EFF of the first peak P_1,A, at the wavelength ^_A. Referring to Fig.4b, the method may comprise vibrating the mirror M2 within the range of d_GAP,AVE - ^d_VIB to d_GAP,AVE + ^d_VIB during the averaging time period ^t_AVE. The mirror M2 may be e.g. vibrated in order to increase the effective spectral width ^ ^_2,A,EFF of the spectral transmittance peak P_2,A at the wavelength ^_A. The method may comprise controlling the position of a mirror M2, with respect to the other mirror M1, by vibrating the mirror M2, near an average mirror gap value d_GAP,AVE (e.g. d_GAP,2), so as to increase the effective spectral width ^ ^_EFF. The mirror gap d_GAP may be changed to the range of d_GAP,AVE - ^d_VIB to d_GAP,AVE + ^d_VIB, before vibrating the mirror M2 during the averaging time period ^t_AVE. The mirror gap d_GAP may be changed out of the range of d_GAP,AVE - ^d_VIB to d_GAP,AVE + ^d_VIB, after the mirror M2 has been vibrated during the averaging time period ^t_AVE. The method may also comprise stopping the movement of the mirror M2 several times during the averaging time period ^t_AVE, so as to vibrate the mirror M2 within the range of d_GAP,AVE - ^d_VIB to d_GAP,AVE + ^d_VIB. Fig.4c shows, by way of example, a probability density function f_P(d_GAP) of the mirror gap values d_GAP during the averaging time period ^t_AVE. All mirror gap values d_GAP may be within the range of d_GAP,AVE - ^d_VIB to d_GAP,AVE + ^d_VIB during the averaging time period ^t_AVE. The mirror M2 may be vibrated during the averaging time period ^t_AVE e.g. so that the average value of the mirror gap is equal to the value d_GAP,2. The mirror M2 may be vibrated during the averaging time period ^t_AVE e.g. so that the most probable value of the mirror gap is equal to the mirror gap value d_GAP,2. f_P,MAX denotes the maximum value of the probability density function f_P(d_GAP). The mirror gap d_GAP may be controlled e.g. according to a sequence of mirror gap values during the averaging time period ^t_AVE. The sequence may be a predetermined sequence. The sequence may be retrieved from a memory e.g. as lookup table. The mirror gap values may exhibit e.g. normal distribution, Weibull distribution, lognormal distribution, or random distribution. The sequence may also be generated in real time according to a suitable random number generator to provide a suitable distribution of mirror gap values. The vibration of the mirror M2 may be periodic and/or irregular. The term vibrating may also include causing non-periodic movement, e.g. according to a random distribution of mirror gap values. Fig 5a shows the first peak P_1,A, the second peak P_2,A, and the third peak P_1,C, in a situation where the effective spectral width ^ ^_EFF of the second peak P_2,A is increased by varying the mirror gap d_GAP in the vicinity of the second mirror gap value d_GAP,2. In particular, the mirror gap d_GAP may be varied near the second mirror gap value d_GAP,2 such that the effective spectral width ^ ^_EFF of the second peak P_2,A is equal to the effective spectral width ^ ^_EFF of the first peak P_1,A. Referring to Fig. 5b, the method may comprise providing a modified spectral transmittance function T_2,MOD( ^) by a linear combination of the first spectral transmittance function T₁( ^) and the second spectral transmittance function T₂( ^). The mirror gap d_GAP may be varied such that the effective spectral width ^ ^_EFF of the second peak P_2,A is equal to the effective spectral width ^ ^_EFF of the first peak P_1,A. The coefficients of the linear combination may be selected such that the modified spectral transmittance function T_2,MOD( ^) does not comprise a spectral transmittance peak at the first wavelength ^_A. The coefficients of the linear combination may be selected such that the peaks P_1,A and P_2,A are substantively eliminated from the modified spectral transmittance function T_2,MOD( ^). The coefficients of the linear combination may be selected such that the modified spectral transmittance function T_2,MOD( ^) comprises only one peak at the second wavelength ^_C. For example, the first mirror gap d_GAP,1 may be selected such that first spectral transmittance function T₁( ^) has only one (first) spectral transmittance peak P_1,A, which corresponds to operation in the first interference order (m=1). The first spectral transmittance peak P_1,A is at a first wavelength ^_A, which corresponds to the mirror gap d_GAP,1, and which corresponds to the first order of interference m=1. The second mirror gap dGAP,2 is greater than the first mirror gap dGAP,1. For example, the second mirror gap dGAP,2 may be e.g. equal to two times the first mirror gap dGAP,1. For example, the second mirror gap dGAP,2 may be selected such that second spectral transmittance function T2( ^) has a second spectral transmittance peak P2,A, which corresponds to operation in the second interference order (m=2), and a third spectral transmittance peak P1,C, which corresponds to operation in the first interference order (m=1). The second spectral transmittance peak P2,A is at the first wavelength ^A, which corresponds to the mirror gap dGAP,2 and which corresponds to the second order of interference (m=2). _{^ ^^ =} ^{^^ ^^ ^^ ^^,2 ^^} 2_{∙ ^^ =} ^{^^ ^^ ^^,2} 2_∙2 ^(2b) The second mirror gap dGAP,2 may be e.g. equal to two times the first mirror gap dGAP,1, so that the second spectral transmittance peak P2,A may coincide with the wavelength ^A of the first spectral transmittance peak P1,A, wherein the first mirror gap dGAP,1 corresponds to the first order of interference (m=1) at the first wavelength ^A, and wherein the second mirror gap dGAP,2 corresponds to the second order of interference (m=2) at the first wavelength ^A. The second spectral transmittance function T2( ^) may further comprise another (third) spectral transmittance peak P1,C at a second wavelength ^C. The (third) spectral transmittance peak P1,C may correspond to operation in the first interference order (m=1). The third spectral transmittance peak P1,C is at the second wavelength ^C, which corresponds to the second mirror gap dGAP,2 and the order of interference m=1. The second wavelength ^_C may be equal to two times the first wavelength ^_A, i.e. ^_C=2 ^ ^_A. The method may comprise forming a modified second spectral transmittance function T_2,MOD( ^) by eliminating the second spectral transmittance peak P_2,A from the second spectral transmittance function T₂( ^). The modified second spectral transmittance function T_2,MOD( ^) may be formed as a linear combination of the first spectral transmittance function T₁( ^) and the second spectral transmittance function T₁( ^). where c₁ and c₂ denote normalization coefficients (i.e. constants). The second spectral transmittance peak P_2,A is spectrally broadened such that the effective spectral width ^ ^_2,A of the second spectral transmittance peak P_2,A is equal to the effective spectral width ^ ^_1,A of the first spectral transmittance peak P_1,A. The normalization coefficients c₁ and c₂ may be selected so as to substantially completely eliminate the second spectral transmittance peak P_2,A, e.g. to fulfill the following criterion: The half width w_N of the integration range may be e.g. in the range of 10% to 40% of the free spectral range ^ ^_FSR. Fig. 6 shows, by way of example, varying the mirror gap d_GAP as a function of time t. The mirror gap d_GAP may be changed e.g. from a minimum value d_GAP,MIN to a maximum value d_GAP,MAX. The minimum value d_GAP,MIN may be determined e.g. so as to reduce or avoid the risk of accidental contact between the mirrors M1, M2. The mirror gap d_GAP may be kept above a forbidden region REG0, so as to avoid damaging the mirrors M1, M2. The mirror gap d_GAP may be changed e.g. at a substantially constant velocity in a first scanning region REG1, e.g. between times t₁₁ and t₂₁. The first scanning region REG1 may be e.g. the region from 1.0 ^d_GAP,MIN to 2.0 ^d_GAP,MIN. The mirror gap d_GAP may be varied at a varying velocity in a second scanning region REG2, so as to equalize the effective spectral widths of the peaks. The second scanning region REG2 may be e.g. the region from 2.0 ^d_GAP,MIN to 2.5 ^d_GAP,MIN. The mirror M2 may be moved in the second scanning region REG2 e.g. between times t₂₁ and t₃₁. In an embodiment, the velocity of the second mirror M2 may be changed e.g. by more than 50% during the averaging time period ^t_AVE. The averaging time period ^t_AVE may be e.g. in the range of 100 ^s to 100 ms. In an embodiment, the mirror M2 may be moved back and forth in the axial direction AX1 in the second scanning region REG2. The mirror M2 may be moved back and forth in the axial direction AX1 during the averaging time period ^t_AVE in the second scanning region REG2. The mirror M2 may be vibrated during the averaging time period ^t_AVE. The mirror gap d_GAP has different values d_GAP(t_A), d_GAP(t_B), d_GAP(t_C), d_GAP(t_D) at scanning times t_A, t_B, t_C, t_D, respectively. The values d_GAP(t_A), d_GAP(t_B) may be in the first scanning region REG1. The values d_GAP(t_C), d_GAP(t_D) may be in the second scanning region REG2. The value d_GAP(t_A) may be smaller than the value d_GAP(t_C). The smaller mirror gap value d_GAP(t_A) attained at the first time t_A may be called e.g. as the first mirror gap d_GAP,1. The greater mirror gap value d_GAP(t_C) attained at the second time t_C may be called e.g. as the second mirror gap d_GAP,2. The Fabry-Perot interferometer FP1 may have a first spectral transmittance function T₁( ^) at the first time t_A, corresponding to the first mirror gap d_GAP,1. The Fabry-Perot interferometer FP1 may have a second spectral transmittance function T₂( ^) at the second time t_C, corresponding to the second mirror gap d_GAP,2. The Fabry-Perot interferometer FP1 may have a third spectral transmittance function T₃( ^) at the time t_B, corresponding to the mirror gap d_GAP(t_B). The Fabry-Perot interferometer FP1 may have a fourth spectral transmittance function T₄( ^) at the time t_D, corresponding to the mirror gap d_GAP(t_D). Figs.7a to 7d show the spectral transmittance functions T( ^) of the Fabry-Perot interferometer FP1 at the times t_A, t_B, t_C, t_D. Referring to Fig. 7a, the transmittance function T₁( ^) of the Fabry-Perot interferometer FP1 may have only one peak P_1,A at the first wavelength ^_A corresponding to the first order of interference (m=1) at the first mirror gap d_GAP,1 at the time t_A. Referring to Fig. 7b, the transmittance function T₃( ^) of the Fabry-Perot interferometer FP1 may have only one peak P_1,B at the wavelength ^_B corresponding to the first order of interference (m=1) at the mirror gap d_GAP at the time t_B. Referring to Fig. 7c, the transmittance function T₂( ^) of the Fabry-Perot interferometer FP1 may have a second peak P_1,C at the second wavelength ^_C corresponding to the first order of interference (m=1) at the second mirror gap d_GAP,2 at the time t_C, and the transmittance function T₂( ^) of the Fabry-Perot interferometer FP1 may have a third peak P_2,A at the first wavelength ^_A corresponding to the second order of interference (m=2) at the second mirror gap d_GAP,2 at the time t_C. Referring to Fig. 7d, the transmittance function T₄( ^) of the Fabry-Perot interferometer FP1 may have a peak P_1,D at the wavelength ^_D corresponding to the first order of interference (m=1) at the mirror gap d_GAP at the time t_D, and the transmittance function T₂( ^) of the Fabry-Perot interferometer FP1 may have a peak P_2,B at the wavelength ^_B corresponding to the second order of interference (m=2) at the mirror gap d_GAP at the time t_D. Referring to Fig.8a, a modified spectral transmittance function T_2,MOD( ^) of the Fabry-Perot interferometer FP1 may be provided as a linear combination of the first spectral transmittance function T₁( ^) of Fig. 7a and the second spectral transmittance function T₂( ^) of Fig. 7c. The modified spectral transmittance function T_2,MOD( ^) may be provided such that the peaks at the first wavelength ^_A are substantially eliminated. The modified spectral transmittance function T_2,MOD( ^) may have only one spectral transmittance peak P_1,C at the second wavelength ^_C. The modified spectral transmittance function T_2,MOD( ^) may be provided such that the peaks P_1,A, P_2,A at the first wavelength ^_A are substantially eliminated. The modified spectral transmittance function T_2,MOD( ^) may be provided such that the peak P_1,A of the first order of interference (m=1) substantially cancels the peak P_2,A of the second order of interference (m=2) at the first wavelength ^_A. In general, a first spectral transmittance function T₁( ^) may be provided at a first mirror gap value, a second spectral transmittance function T₂( ^) may be provided by controlling the mirror gap in the vicinity of a second greater mirror gap value, the modified spectral transmittance function T_2,MOD( ^) may be provided as a linear combination of the first spectral transmittance function T₁( ^) and the second spectral transmittance function T₂( ^), wherein the modified spectral transmittance function T_2,MOD( ^) may be provided such that the peak P_1,A of a lower order of interference (m_L) substantially cancels the peak P_2,A of a higher order of interference (m_H) at the first wavelength ^_A. Referring to Fig.8b, a modified spectral transmittance function T_4,MOD( ^) of the Fabry-Perot interferometer FP1 may be provided as a linear combination of the spectral transmittance function T₃( ^) of Fig. 7b and the spectral transmittance function T₄( ^) of Fig.7d. The modified spectral transmittance function T_4,MOD( ^) may have only one spectral transmittance peak P_1,D at the wavelength ^_D. Fig.9 shows, by way of example, method steps for providing a modified spectral transmittance function. A first spectral transmittance function T₁( ^) may be provided at a first mirror gap d_GAP,1 such that the first spectral transmittance function T₁( ^) has a first spectral transmittance peak P_1,A at a first wavelength ^_A (step 1010). A second spectral transmittance function T₂( ^) may be provided at a second mirror gap d_GAP,2 such that the second spectral transmittance function T₂( ^) has a second spectral transmittance peak P_2,A at the first wavelength ^_A, and a third spectral transmittance peak P_1,C at a second wavelength ^_C (step 1020). The second mirror M₂ of the Fabry-Perot interferometer FP1 may be moved and/or tilted such that the effective spectral width ^ ^_2,A,EFF of the second spectral transmittance peak P_2,A at the first wavelength ^_A becomes equal to the effective spectral width ^ ^_1,A,EFF of the first spectral transmittance peak P_1,A at the first wavelength ^_A (step 1030). The modified spectral transmittance function T_2,MOD( ^) may be provided as a linear combination of the first spectral transmittance function T₁( ^) and the second spectral transmittance function T₂( ^) (step 1040). The modified spectral transmittance function T_2,MOD( ^) may be provided such that the peak P_1,A of the lower order of interference (m_L) substantially cancels the peak P_2,A of the higher order of interference (m_H) at the first wavelength ^_A. Figs.10a to 10d illustrate selecting suitable mirror gap regions REG1, REG2 for obtaining the first spectral transmittance function T₁( ^) and the second spectral transmittance function T₂( ^). The solid inclined lines indicate the spectral position ^_PEAK of a spectral transmittance peak P as the function of the mirror gap d_GAP for each order of interference m=1, m=2, m=3, m=4, m=5. Referring to Fig.10a, a first spectral transmittance function T₁( ^) may be obtained by selecting a first mirror gap d_GAP which is within a first scanning region REG1. A second spectral transmittance function T₂( ^) may be obtained by selecting a second different mirror gap d_GAP which is within a second scanning region REG2. The first scanning region REG1 may be selected so as to ensure that the first spectral transmittance function T₁( ^) has the first peak P_1,A at the first wavelength ^_A. The second scanning region REG2 may be selected so as to ensure that the second spectral transmittance function T₂( ^) has the second peak P_2,A at the first wavelength ^_A, and the third peak P_1,C at the second wavelength ^_C. The scanning region REG2 and the measurement range MSR1 may be selected so as to ensure that the second spectral transmittance function T₂( ^) has only two peaks. The first peak P_1,A and the third peak P_1,C may correspond e.g. to the first order of interference (m=1), and the second peak P_2,A may correspond to the second order of interference (m=2). Thus, the first peak P_1,A of the first order of interference (m=1) may be used to cancel the second peak P_2,A of the second order of interference (m=2) so that only the third peak P_1,C of the first order of interference (m=1) remains at the second wavelength ^_C. This embodiment may provide an extended measurement range MSR1. A transmittance peak of a lower order of interference (e.g. m_L=1) may be used to cancel a transmittance peak of a higher order of interference (e.g. m_H=2). The measurement range MSR1 may comprise spectral sub-ranges RNG1, RNG2. The sub-range RNG1 may be e.g. the spectral range for the transmittance peak of the lower order of interference (e.g. m=1), in the situation where the mirror gap d_GAP is within the first scanning region REG1. The sub-range range RNG2 may be e.g. the spectral range for the transmittance peak of the lower order of interference (e.g. m=1), in the situation where the mirror gap d_GAP is within the second scanning region REG2. Referring to Figs.10b and 10c, a first spectral transmittance function T₁( ^) may be obtained by selecting a first mirror gap d_GAP which is within a first scanning region REG1. A second spectral transmittance function T₂( ^) may be obtained by selecting a second different mirror gap d_GAP which is within a second scanning region REG2. The first scanning region REG1 may be selected so as to ensure that the first spectral transmittance function T₁( ^) has the first peak P_2,A at the first wavelength ^_A. The second scanning region REG2 may be selected so as to ensure that the second spectral transmittance function T₂( ^) has the second peak P_3,A at the first wavelength ^_A, and the third peak P_2,C at the second wavelength ^_C. The measurement range MSR1 may be selected so as to ensure that the second spectral transmittance function T₂( ^) has only two peaks. The first peak P_2,A and the third peak P_2,C may correspond e.g. to the second order of interference (m=2), and the second peak P_3,A may correspond to the third order of interference (m=3). Thus, the first peak P_2,A of the second order of interference (m=2) may be used to cancel the second peak P_3,A of the third order of interference (m=3) so that only the third peak P_2,C of the second order of interference (m=2) remains at the second wavelength ^_C. This embodiment may provide improved spectral resolution. A transmittance peak of a lower order of interference (e.g. m_L=2) may be used to cancel a transmittance peak of a higher order of interference (e.g. m_H=3). The first scanning region REG1 may be selected such that the first spectral transmittance function T₁( ^) has only one transmittance peak in a situation where the mirror gap d_GAP is within the first scanning region REG1. The scanning region REG2 may be selected such that the second spectral transmittance function T₂( ^) has only two transmittance peaks in a situation where the mirror gap d_GAP is within the scanning region REG2. The transmittance peak of the first spectral transmittance function T₁( ^) may be used to cancel one of the transmittance peaks of the second spectral transmittance function T₂( ^), so that only the other transmittance peak of the second spectral transmittance function T₂( ^) remains. The measurement range MSR1 may comprise spectral sub-ranges RNG1, RNG2. The sub-range RNG1 may be the spectral range for the transmittance peak of the second order of interference (m=2), in the situation where the mirror gap d_GAP is within the first scanning region REG1. The sub-range range RNG2 may be the spectral range for the transmittance peak of the second order of interference (m=2), in the situation where the mirror gap d_GAP is within the second scanning region REG2. Referring to Fig.10d, a first spectral transmittance function T₁( ^) may be obtained by selecting a first mirror gap d_GAP which is within a first scanning region REG1. A second spectral transmittance function T₂( ^) may be obtained by selecting a second different mirror gap d_GAP which is within an auxiliary scanning region REG3. The first scanning region REG1 may be selected so as to ensure that the first spectral transmittance function T₁( ^) has the first peak P_2,A at the first wavelength ^_A. The auxiliary scanning region REG3 may be selected so as to ensure that the second spectral transmittance function T₂( ^) has the second peak P_4,A at the first wavelength ^_A, and the third peak P_3,C at the second wavelength ^_C. The first peak P_2,A may correspond e.g. to the second order of interference (m=2), the second peak P_4,A may correspond e.g. to the fourth order of interference (m=4), and the third peak P_3,C may correspond e.g. to the third order of interference (m=3). Thus, the first peak P_2,A of the second order of interference (m=2) may be used to cancel the second peak P_4,A of the fourth order of interference (m=4) so that only the third peak P_3,C of the third order of interference (m=3) remains at the second wavelength ^_C. The first peak P_2,A and the second peak P_4,A may be in a spectral range RNG4. The third peak P_3,C may be in a spectral range RNG3. This embodiment may provide improved spectral resolution at least in the measurement sub-range RNG3. The sub-range RNG3 is the spectral range for the transmittance peak of the third order of interference (m=3), in the situation where the mirror gap d_GAP is within the auxiliary scanning region REG3. The range RNG4 is the spectral range for the transmittance peak of the fourth order of interference (m=4), in the situation where the mirror gap d_GAP is within the auxiliary scanning region REG3. A transmittance peak of a lower order of interference (e.g. m_L=2) may be used to cancel a transmittance peak of a higher order of interference (e.g. m_H=4). The first scanning region REG1 may be selected such that the first spectral transmittance function T₁( ^) has only one transmittance peak in a situation where the mirror gap d_GAP is within the first scanning region REG1. The scanning region REG3 may be selected such that the second spectral transmittance function T₂( ^) has only two transmittance peaks in a situation where the mirror gap d_GAP is within the scanning region REG3. The transmittance peak of the first spectral transmittance function T₁( ^) may be used to cancel one of the transmittance peaks of the second spectral transmittance function T₂( ^), so that only the other transmittance peak of the second spectral transmittance function T₂( ^) remains. One or more further measurement sub-ranges RNG1, RNG2 may be implemented e.g. as discussed with reference to Fig.10c, if desired. Referring to Fig. 11a, the Fabry-Perot interferometer FP1 may optionally comprise e.g. three actuators ACU1a, ACU1b, ACU1c. The actuators ACU1a, ACU1b, ACU1c may enable tilting the mirror M2 e.g. about the a second axis AX2 and about a third axis AX3. The second axis AX2 may be e.g. parallel with the direction SX, and the third axis AX3 may be parallel with the direction SY. The optical axis AX1 may be parallel with the direction SZ and perpendicular to the first mirror M1. SX, SY and SZ denote orthogonal directions. The Fabry-Perot interferometer FP1 may optionally comprise sensors CAP1a, CAP1b, CAP1c for monitoring the mirror gap d_GAP and/or for monitoring the tilt angle ^₂ of the second mirror M2. The sensors may be e.g. capacitive sensors. The mirror gap d_GAP may be varied e.g. by adding a vibrating component to a control signal (S_ACU1) of the actuators ACU1a, ACU1b, ACU1c. The mirror M2 may be tilted by adding a tilting component to a control signal of the actuators ACU1a, ACU1b, ACU1c. In an embodiment, the mirror gap d_GAP is controlled by closed loop control, by using a feedback signal obtained from the sensors CAP1a, CAP1b, CAP1c. The mirror gap d_GAP may also be varied e.g. by adding a vibrating component to a feedback signal obtained from the sensors CAP1a, CAP1b, CAP1c. The mirror M2 may also be tilted e.g. by adding a tilting component to the feedback signal obtained from the sensors CAP1a, CAP1b, CAP1c. Referring to Fig.11b, the control unit CNT1 of the Fabry-Perot interferometer FP1 may form one or more control signals S_ACU1a, S_ACU1b for driving the actuators ACU1a, ACU1b, so as to set the mirror gap d_GAP and/or the tilt angle ^₂ of the mirror M2. The control unit CNT1 may receive one or more feedback signals S_FB1a, S_FB1b formed by using distance sensors CAP1a, CAP1b. The feedback signal S_FB1a, S_FB1b may be indicative of the distance between the mirrors M1, M2. The one or more control signals S_ACU1a, S_ACU1b may be e.g. digital signals. The one or more feedback signals S_FB1a, S_FB1b may be e.g. digital signals. The distance sensors CAP1a, CAP1b may be e.g. capacitive sensors. The sensor CAP1a for measuring mirror gap d_GAP may comprise electrodes E1a, E2a, E3a. The electrodes E1a, E2a may form a first capacitor, and the electrodes E2a, E3a may form a second capacitor. The sensor CAP1a may comprise the first capacitor and the second capacitor, which are connected in series. The electrodes E1a, E3a may be attached to a stationary mirror plate PLA1, and the electrode E2a may be attached to a moving mirror plate PLA2. The apparatus 500 may comprise a distance measuring unit DMU1, which may be arranged to form the feedback signal S_FB1a by measuring the capacitance of the sensor CAP1a. The distance measuring unit DMU1 may be connected to the electrodes E1a, E3a via conductors CON1, CON2. The distance measuring unit DMU1 may measure the capacitance of the sensor CAP1 e.g. by coupling a current signal IM1 to the electrodes E1a, E3a, and by monitoring the corresponding voltage signal VM1 over the electrodes E1a, E3a. Alternatively, the distance measuring unit DMU1 may measure the capacitance of the sensor CAP1 e.g. by coupling a voltage signal VM1 over the electrodes E1a, E3a, and by monitoring the corresponding current signal IM1 of the electrodes E1a, E3a. The capacitance of the sensor CAP1a may be indicative of the distance between the electrodes E1a, E2a. The capacitance of the sensor CAP1a may be indicative of the distance between the mirrors M1, M2. The feedback signal S_FB1a may be indicative of the distance between the electrodes E1a, E2a. The feedback signal S_FB1a may be indicative of the distance between the mirrors M1, M2. The second sensor CAP1b for measuring the mirror gap d_GAP may comprise electrodes E1b, E2b, E3b. The sensors CAP1a, CAP1b may together measure also a tilt angle ^₂ of the second mirror M2. A distance measuring unit DMU1 may form the feedback signal S_FB1b by measuring the capacitance of the sensor CAP1b. The Fabry-Perot interferometer may comprise a driving unit DRV1 to form a driving signal HV1 according to the control signal S_ACU1a. The driving signal may be e.g. a high voltage signal. The driving unit DRV1 may form a high voltage driving signal HV1 according to the digital control signal S_ACU1a. The actuator ACU1a may be e.g. a piezoelectric actuator or an electrostatic actuator. The high voltage signal HV1 may be connected to the actuator ACU1a via conductors CON1, CON2. The Fabry-Perot interferometer FP1 may comprise a second driving unit DRV1 for driving a second actuator ACU1b according to the control signal S_ACU1b. Referring to Figs.11a and 11c, the optical axis AX1 is parallel with the direction SZ, a second axis AX2 is parallel with the direction SX, and a third axis SX3 is parallel with the direction SY. The Fabry-Perot interferometer FP1 may be arranged to tilt the mirror M2 about the second axis AX2, and also about the third axis AX3. In particular, the three actuators ACU1a, ACU1b, ACU1c may be driven in a phased fashion with a 120 ^ phase difference such that the normal N2 of the second mirror M2 may rotate about the optical axis AX1. Referring to Figs. 12a to 12d, a spectroscopic apparatus 500 may comprise a Fabry-Perot interferometer FP1, a control unit CNT1, and a detector SEN1. The detector SEN1 may be arranged to detect light according to the averaging time period ^t_AVE. The detector SEN1 may be arranged to operate such that the exposure time period of the detector SEN1 is equal to the averaging time period ^t_AVE. The averaging time period ^t_AVE may be e.g. in the range of 100 ^s to 100 ms. The averaging time period ^t_AVE may be e.g. in the range of 1 ms to 100 ms. Referring to Fig.12a, the apparatus 500 may be a spectrometer, which comprises a Fabry-Perot interferometer FP1, a control unit CNT1, and a detector SEN1. The apparatus 500 may receive input light B1 e.g. from an object OBJ1. The input light B1 may have one or more spectral components, e.g. at the wavelengths ^_A and ^_C. The input light B1 may have a spectral intensity distribution I_B1( ^), i.e. the spectrum I_B1( ^). The apparatus 500 may be arranged to measure the spectral intensity distribution I_B1( ^) of the input light B1. The Fabry-Perot interferometer FP1 may be used as a tunable narrowband filter, which allows one or two spectral components of the input light B1 to pass as transmitted light B2 to the detector SEN1. The Fabry-Perot interferometer FP1 forms transmitted light B2 by filtering input light B1 e.g. according to the spectral transmittance function T₁( ^) or T₂( ^) of the Fabry-Perot interferometer FP1. The detector SEN1 measures the intensity of the light B2 transmitted through the Fabry-Perot interferometer FP1. The detector SEN1 forms a signal S_SEN1 indicative of the intensity of the transmitted light B2. The control unit CNT1 may control the position of the mirror M2. The control unit CNT1 may also calculate output intensity values from measured intensity values obtained from the detector SEN1. For example, the control unit CNT1 may: - set the mirror gap (d_GAP) to a first mirror gap value (d_GAP,1) to provide a first spectral transmittance peak (P_1,A) at a first wavelength ( ^_A), wherein the first spectral transmittance peak (P_1,A) has an effective spectral width ( ^ ^_1,A,EFF), - change the mirror gap (d_GAP) to a second different mirror gap value (d_GAP,2) to provide a second spectral transmittance peak (P_2,A) at the first wavelength ( ^_A), and a third spectral transmittance peak (P_1,C) at a second wavelength ( ^_C), and - control the position of a mirror (M2) of the Fabry-Perot interferometer (FP1) such that the effective spectral width ( ^ ^_2,A,EFF) of the second spectral transmittance peak (P_2,A) is substantially equal to the effective spectral width ( ^ ^_1,A,EFF) of the first spectral transmittance peak (P_1,A). The signal obtained from the detector SEN1 at the second mirror gap value (d_GAP,2) may comprise contributions of two different spectral components of the input light B1, corresponding to the second transmittance peak and the third transmittance peak. The contribution of light transmitted via the second transmittance peak may be eliminated by calculating the linear combination of the detector signals, so that the linear combination may represent only the intensity of light transmitted via the third transmittance peak. For example, the control unit CNT1, or another data processor of the apparatus, may be arranged to: - obtain a first intensity value (I₁) by using the detector (SEN1) when the mirror gap (d_GAP) is set to the first mirror gap value (d_GAP,1), - obtain a second intensity value (I₂) by using the detector (SEN1) when the mirror gap (d_GAP) is set to the second mirror gap value (d_GAP,2), and - calculate a third intensity value (I_2,C) as a linear combination of the first intensity value (I₁) and the second intensity value (I₂), wherein the third intensity value (I_2,C) represents the spectral intensity (I_{B2, ^C}) of the transmitted light (B2) at the second wavelength ( ^_C). The mirror gap d_GAP may be optionally scanned over a suitable scanning region, and the above-mentioned steps may be repeated to calculate a complete spectral intensity distribution I_B1( ^) of the input light B1. The calculated spectral intensity distribution I_B1( ^) may cover e.g. the whole spectral measurement range MSR1, or a selected sub-range of the spectral measurement range MSR1. The control unit CNT1 may control the position of the mirror M2 by sending control signals S_ACU1 to the Fabry-Perot interferometer FP1. The control signal S_ACU1 may be e.g. indicative of a target position of the mirror M2. The Fabry-Perot interferometer FP1 may optionally provide a feedback signal S_FB1 indicative of the actual measured position of the mirror M2. The Fabry-Perot interferometer FP1 may optionally comprise a driving unit (DRV1) to convert a digital control signal S_ACU1 into an analog signal, which is coupled to the actuator ACU1. In particular, the Fabry-Perot interferometer FP1 may comprise a driving unit (DRV1) to convert a digital control signal S_ACU1 into a high voltage driving signal (HV1), which is coupled to drive a piezoelectric actuator ACU1 or to drive an electrostatic actuator ACU1. The Fabry-Perot interferometer FP1 may optionally comprise one or more sensors (CAP1) to measure the actual mirror gap d_GAP. The Fabry-Perot interferometer FP1 may optionally comprise a measuring unit (DMU1) to provide a feedback signal S_FB1 indicative of the measured mirror gap d_GAP. The measuring unit (DMU1) may e.g. form a feedback signal S_FB1, which is indicative of a measured capacitance of a capacitive distance sensor, which comprises two or more sensor electrodes E2a, E2b, E2c. The capacitance of the distance sensor may depend on the actual mirror gap d_GAP. The apparatus 500 may comprise one or more filters FIL1, FIL2 to define the spectral measurement range MSR1. The filters FIL1, FIL2 may be positioned in front of and/or behind the Fabry-Perot interferometer FP1. The one or more filters may be positioned on the optical path of the Fabry-Perot interferometer FP1. The lower limit ^_LP and/or the upper limit ^_SP of the measurement range MSR1 may be defined by the one or optical filters. The one or more filters may be arranged to provide a spectral transmittance function T_CUT( ^), for defining the measurement range MSR1. The filters FIL1, FIL2 may also be omitted if optical properties of the other components of the apparatus 500 define the spectral measurement range MSR1. The control unit CNT1 may also be arranged to perform signal processing operations with the measured intensity of the transmitted light B2. The apparatus 500 may comprise a memory MEM1 for storing measured intensity values, which are obtained from the detector SEN1. The measured intensity values may be stored as intensity data DATA1. The apparatus 500 may comprise a memory MEM2 for storing calculated intensity values, which may be obtained as linear combinations of measured intensity values. The calculated intensity values may be stored as output data OUT1. The apparatus 500 may comprise a memory MEM3 for storing calibration parameters PAR1. The calibration parameters PAR1 may specify e.g. a relation between control signal values S_ACU1 and wavelengths ^_PEAK of the transmittance peaks. The calibration parameters PAR1 may specify e.g. a relation between feedback signal values S_FB1 and wavelengths ^_PEAK of the transmittance peaks. The apparatus 500 may comprise a memory MEM4 for storing computer program code PROG1. When running on the control unit CNT1, the program code PROG1 may be arranged to execute the method steps for moving the mirror M2, for obtaining measured intensity values from the detector SEN1 and/or for calculating output intensity values from the measured intensity values. The apparatus 500 may comprise a communication unit RXTX1 for receiving and/or sending data by wired and/or wireless communication, e.g. via a mobile communications network (e.g. 4G, 5G) or via a wireless local area network (WLAN). For example, the apparatus 500 may send output data OUT1 to an internet server by using the communication unit RXTX1. In an embodiment, signal processing may also be performed in a distributed manner in a remote device, e.g. in a portable computer, which is arranged to communicate with the apparatus 500 via the communication unit RXTX1. For example, the computer may be arranged to calculate a third intensity value (I_2,C) as a linear combination of the first intensity value (I₁) and the second intensity value (I₂). The apparatus 500 may comprise a user interface UIF1 for receiving user input and/or for providing information to a user. The user interface UIF1 may be implemented e.g. by a touchscreen. The user interface UIF1 may also be implemented e.g. by an application running on a smartphone or on a portable computer. Referring to Fig.12b, the apparatus 500 may further comprise an illuminating unit ILU1 to illuminate an object OBJ1 with the narrowband tunable light B2, which is transmitted via the Fabry-Perot interferometer FP1. The illuminating unit ILU1 may comprise a light source LS1 and the Fabry-Perot interferometer FP1. The object OBJ1 may provide reflected light B3 e.g. by reflecting the illuminating light B2. The detector SEN1 may receive the reflected light B3, and the detector SEN1 may measure the intensity of the reflected light B3. The apparatus 500 may be arranged to: - obtain a first intensity value (I₁) by using the detector (SEN1) when the mirror gap (d_GAP) is set to the first mirror gap value (d_GAP,1), - obtain a second intensity value (I₂) by using the detector (SEN1) when the mirror gap (d_GAP) is set to the second mirror gap value (d_GAP,2), - calculate a third intensity value (I_2,C) as a linear combination of the first intensity value (I₁) and the second intensity value (I₂), wherein the third intensity value (I_2,C) represents the spectral intensity (I_{B3, ^C}) of the reflected light (B3) at the second wavelength ( ^_C), and - calculate a spectral reflectance value of the object (OBJ1) from the third intensity value (I_2,C). Thus, the apparatus 500 may be arranged to calculate spectral reflectance of the object OBJ1 as linear combination of detector signals. Referring to Fig.12c, the detector SEN1 may also be an image sensor, and the apparatus 500 may further comprise imaging optics LNS1 to form an optical image IMG1 of the object OBJ1 on the image sensor SEN1. The apparatus 500 may be a spectral imaging device. The apparatus 500 may be a hyperspectral imager. The imaging optics LNS1 may be arranged to focus the transmitted light B2 to the image sensor SEN1. The imaging optics LNS1 may comprise e.g. one or more lenses, which may be positioned in front of and/or behind the Fabry-Perot interferometer FP1. The apparatus 500 may be arranged to: - capture a first image of the object (OBJ1) at the first wavelength ( ^_A) by using the image sensor (SEN1) when the mirror gap (d_GAP) is set to the first mirror gap value (d_GAP,1), - capture a second image of the object (OBJ1) by using the image sensor (SEN1) when the mirror gap (d_GAP) is set to the second mirror gap value (d_GAP,2), wherein the second image comprises contributions of spectral components at the first wavelength ( ^_A) and at the second wavelength ( ^_C), and - calculate a third image of the object (OBJ1) as a linear combination of the first image and the second image, wherein the third image represents a spectral component of the object (OBJ1) at the second wavelength ( ^_C). The image sensor SEN1 may be a panchromatic image sensor. The panchromatic image sensor comprises a two-dimensional array of detector pixels, wherein each detector pixel may have substantially similar spectral sensitivity function. The spectral sensitivity of each detector pixel of the panchromatic image sensor SEN1 may be greater than zero over the whole spectral measurement range MSR1 of the apparatus 500. Referring to Fig.12d, the spectral imaging device 500 may further comprise an illuminating unit ILU1 to illuminate the object OBJ1 with the narrowband tunable light B2, which is transmitted via the Fabry-Perot interferometer FP1. The illuminating unit ILU1 may comprise a light source LS1 and the Fabry-Perot interferometer FP1. The object OBJ1 may provide reflected light B3 e.g. by reflecting the illuminating light B2. The imaging optics LNS1 may subsequently form an image IMG1 of the object OBJ1 on the image sensor SEN1. The imaging optics LNS1 may focus the reflected light B3 to the image sensor SEN1. B4 may denote focused reflected light. The device 500 may comprise an imaging unit CAM1, which comprises the imaging optics LNS1 and the image sensor SEN1. The apparatus 500 may be arranged to: - capture a first image of the object (OBJ1) at the first wavelength ( ^_A) by using the image sensor (SEN1) when the mirror gap (d_GAP) is set to the first mirror gap value (d_GAP,1), - capture a second image of the object (OBJ1) by using the image sensor (SEN1) when the mirror gap (d_GAP) is set to the second mirror gap value (d_GAP,2), wherein the second image comprises contributions of spectral components at the first wavelength ( ^_A) and at the second wavelength ( ^_C), and - calculate a third image of the object (OBJ1) as a linear combination of the first image and the second image, wherein the third image represents a spectral component of light (B3) reflected from the object (OBJ1) at the second wavelength ( ^_C). In an embodiment, the illuminating unit ILU1 may be used to provide transmitted light B2, which has a controllable effective bandwidth at a predetermined wavelength ^_PEAK in a predetermined order of interference m. The illuminating unit ILU1 may also be used as a separate unit, e.g. without the detector. The effective bandwidth may be determined over the averaging time period ^t_AVE. An illuminating apparatus ILU1 may comprise: - a Fabry-Perot interferometer FP1 having an adjustable mirror gap d_GAP, and - a control unit CNT1 for controlling the mirror gap d_GAP, wherein the apparatus is arranged to: - control the position of a mirror M2 of the Fabry-Perot interferometer such that the effective spectral width of a spectral transmittance peak of the Fabry-Perot interferometer at a first predetermined wavelength ( ^_PEAK) at a predetermined order of interference (m) is equal to a reference value, which is greater than 1.2 times the minimum attainable spectral width of a spectral transmittance peak of the Fabry-Perot interferometer at said first predetermined wavelength ( ^_PEAK) at said predetermined order of interference. In an embodiment, an apparatus 500 for spectral measurements comprises: - a Fabry-Perot interferometer FP1, which has an adjustable mirror gap d_GAP, - an illuminating unit ILU1 to illuminate an object OBJ1 with narrowband tunable light B2, which is transmitted via the Fabry-Perot interferometer FP1, - a control unit CNT1 for controlling the mirror gap d_GAP, - an image sensor SEN1 to detect light B3 reflected from the object OBJ1, wherein the apparatus 500 is arranged to: - set the mirror gap d_GAP to a first mirror gap value d_GAP,1 to provide a first spectral transmittance peak P_1,A at a first wavelength ^_A, wherein the first spectral transmittance peak P_1,A has an effective spectral width ^ ^_1,A,EFF, - capture a first image of the object OBJ1 at the first wavelength ^_A by using the image sensor SEN1 when the mirror gap d_GAP is set to the first mirror gap value d_GAP,1, - change the mirror gap d_GAP to a second different mirror gap value d_GAP,2 to provide a second spectral transmittance peak P_2,A at the first wavelength ^_A, and a third spectral transmittance peak P_1,C at a second wavelength ^_C, - control the position of a mirror M2 of the Fabry-Perot interferometer FP1 by vibrating and/or tilting the mirror M2 near the second different mirror gap value d_GAP,2, so as to increase an effective spectral width ^ ^_2,A,EFF of the second spectral transmittance peak P_2,A such that the effective spectral width ^ ^_2,A,EFF of the second spectral transmittance peak P_2,A is substantially equal to the effective spectral width ^ ^_1,A,EFF of the first spectral transmittance peak P_1,A, - capture a second image of the object OBJ1 by using the image sensor SEN1 when the mirror gap d_GAP is set near the second mirror gap value d_GAP,2, wherein the second image comprises contributions of spectral components at the first wavelength ^_A and at the second wavelength ^_C, and - calculate a third image of the object OBJ1 as a linear combination of the first image and the second image, wherein the third image represents a spectral component of light B3 reflected from the object OBJ1 at the second wavelength ^_C. For the person skilled in the art, it will be clear that modifications and variations of the devices and methods according to the present invention are perceivable. The figures are schematic. The particular embodiments described above with reference to the accompanying drawings are illustrative only and not meant to limit the scope of the invention, which is defined by the appended claims.

Claims

CLAIMS 1. An apparatus (500) for spectral measurements comprises: - a Fabry-Perot interferometer (FP1) having an adjustable mirror gap (d_GAP), and - a control unit (CNT1) for controlling the mirror gap (d_GAP), wherein the apparatus (500) is arranged to: - set the mirror gap (d_GAP) to a first mirror gap value (d_GAP,1) to provide a first spectral transmittance peak (P_1,A) at a first wavelength ( ^_A), wherein the first spectral transmittance peak (P_1,A) has an effective spectral width ( ^ ^_1,A,EFF), - change the mirror gap (d_GAP) to a second different mirror gap value (d_GAP,2) to provide a second spectral transmittance peak (P_2,A) at the first wavelength ( ^_A), and a third spectral transmittance peak (P_1,C) at a second wavelength ( ^_C), and - control the position of a mirror (M2) of the Fabry-Perot interferometer (FP1) near the second different mirror gap value (d_GAP,2) such that the effective spectral width ( ^ ^_2,A,EFF) of the second spectral transmittance peak (P_2,A) is substantially equal to the effective spectral width ( ^ ^_1,A,EFF) of the first spectral transmittance peak (P_1,A). 2. The apparatus (500) of claim 1, being arranged to vary the mirror gap (d_GAP) by vibrating the mirror (M2) of the Fabry-Perot interferometer (FP1), so as to increase the effective spectral width of the second spectral transmittance peak (P_2,A). 3. The apparatus (500) of claim 1 or 2, being arranged to tilt the mirror (M2), so as to increase the effective spectral width of the second spectral transmittance peak (P_2,A). 4. The apparatus (500) according to any of the claims 1 to 3, wherein the effective spectral width ( ^ ^_2,A,EFF) of the second spectral transmittance peak (P_2,A) is the difference ( ^_R,AVE - ^_L,AVE) between a first average spectral position ( ^_R,AVE) and a second average spectral position ( ^_L,AVE), wherein the first average spectral position ( ^_R,AVE) is the average spectral position ( ^_R,AVE) of a first edge of the second spectral transmittance peak (P_2,A), wherein the second average spectral position ( ^_L,AVE) is the average spectral position ( ^_L,AVE) of a second edge of the second spectral transmittance peak (P_2,A), wherein the spectral positions ( ^_R,AVE, ^_L,AVE) of the edges are determined at the half maximum height of said peak (P), wherein the spectral positions ( ^_R,AVE, ^_L,AVE) of the edges are averaged over an averaging time period ( ^t_AVE), and wherein the averaging time period ( ^t_AVE) is in the range of 100 ^s to 100 ms. 5. The apparatus (500) according to any of the claims 1 to 4, comprising a detector (SEN1) to detect light (B2) transmitted through the Fabry-Perot interferometer (FP1), wherein the apparatus (500) is arranged to: - obtain a first intensity value (I₁) by using the detector (SEN1) when the mirror gap (d_GAP) is set to the first mirror gap value (d_GAP,1), - obtain a second intensity value (I₂) by using the detector (SEN1) according to the averaging time period ( ^t_AVE) when the mirror gap (d_GAP) is near the second mirror gap value (d_GAP,2), and - calculate a third intensity value (I_2,C) as a linear combination of the first intensity value (I₁) and the second intensity value (I₂), wherein the third intensity value (I_2,C) represents the spectral intensity (I_{B2, ^C}) of the transmitted light (B2) at the second wavelength ( ^_C). 6. The apparatus (500) of claim 5, wherein the detector (SEN1) is a panchromatic image sensor comprising a two-dimensional array of detector pixels, wherein each detector pixel has substantially similar spectral sensitivity. 7. The apparatus (500) according to any of the claims 1 to 6, wherein the apparatus (500) is a spectral imaging device. 8. The apparatus (500) according to any of the claims 1 to 7, comprising one or more filters (FIL1, FIL2) to define a spectral measurement range (MSR1) of the Fabry-Perot interferometer (FP1), wherein the upper cut-off wavelength ( ^_SP) of the measurement range (MSR1) is greater than 2.0 times the lower cut-off wavelength ( ^_LP) of the measurement range (MSR1), advantageously in the range of 2.1 to 2.5 times the lower cut-off wavelength ( ^_LP). 9. The apparatus (500) according to any of the claims 1 to 8, comprising a light source (LS1) to provide input light (B1), wherein the Fabry-Perot interferometer (FP1) is arranged to form narrowband transmitted light (B2) at the first wavelength ( ^_A) and at the second wavelength ( ^_C) by filtering the input light (B1). 10. A method, comprising: - receiving input light (B1) to a Fabry-Perot interferometer (FP1), which has an adjustable mirror gap (d_GAP), - setting the mirror gap (d_GAP) to a first mirror gap value (d_GAP,1) to provide a first spectral transmittance peak (P_1,A) at a first wavelength ( ^_A), wherein the first spectral transmittance peak (P_1,A) has an effective spectral width ( ^ ^_1,A,EFF), - changing the mirror gap (d_GAP) to a second different mirror gap value (d_GAP,2) to provide a second spectral transmittance peak (P_2,A) at the first wavelength ( ^_A), and a third spectral transmittance peak (P_1,C) at a second wavelength ( ^_C), and - controlling the position of a mirror (M2) of the Fabry-Perot interferometer (FP1) near the second mirror gap value (d_GAP,2) such that the effective spectral width ( ^ ^_2,A,EFF) of the second spectral transmittance peak (P_2,A) is substantially equal to the effective spectral width ( ^ ^_1,A,EFF) of the first spectral transmittance peak (P_1,A). 11. The method of claim 10, wherein the Fabry-Perot interferometer (FP1) has a first spectral transmittance function T₁( ^) having the first spectral transmittance peak (P_1,A) at the first mirror gap value (d_GAP,1), wherein the Fabry-Perot interferometer (FP1) has a second spectral transmittance function T₂( ^) having the second spectral transmittance peak (P_2,A) and the third spectral transmittance peak (P_1,C) near the second mirror gap value (d_GAP,2), wherein the method comprises providing a modified spectral transmittance function T_2,MOD( ^) as a linear combination of the first spectral transmittance function T₁( ^) and the second spectral transmittance function T₂( ^).