A Fiber-Optic Array Spectrometer With Parallel Multichannel Optical Lock-in Detection and its Application to in Situ Lighting Measurements

This article describes a new optical spectroscopy instrument achieving lock-in detection in all its spectral output channels in a parallel and simultaneous fashion. It is based on two identical compact array spectrometers working in phase quadrature thanks to optical modulators synchronized with an external reference signal. In the application example, the optical lock-in spectrometer was used to perform spectral irradiance measurements with commercial LED lamps exhibiting temporal light modulation at different frequencies. A remote sensing optical device was designed to measure from a distance the temporal luminous waveform of a specific LED lamp and send it to the reference input of the optical lock-in spectrometer. When the lamps were operating together on top of a large continuous luminous background, the optical lock-in spectrometer successfully retrieved the respective spectral irradiance distributions and color parameters of each lamp, allowing their characterization to be performed independently of the other light sources illuminating the sensor during the measurements.


I. INTRODUCTION
L OCK-IN detection is a well-known technique to measure the amplitude and phase of a modulated signal in the presence of noise and background signals. This technique is commonly used in many applications to extract small, modulated signals buried in noise that cannot be directly measured [1].
In the field of optical spectroscopy, commercially available lock-in amplifiers are used to improve the signal to noise ratio of spectra obtained with scanning spectrometers equipped with a single detector [2]. Modern optical spectrometers are based on a fixed diffraction grating associated with a CCD or CMOS array detector. They are used in most physical and chemical analytical instruments. Performing lock-in detection with an array detector requires the parallel and simultaneous processing of typically thousands or millions of individual signals, each being associated with a specific pixel, or a block of pixels, corresponding to a single wavelength.
In this article, we present a novel optical spectrometer designed to perform parallel and multichannel lock-in detection. It is based on two compact array spectrometers working in phase quadrature thanks to an optical modulator synchronized with an external reference signal. An application example is given with spectral irradiance measurements performed on a set of commercial lamps exhibiting temporal light modulation at different frequencies. When these lamps are operating together with a large luminous background, the objective of using the optical lock-in spectrometer is to retrieve the respective spectral characteristics of each lamp, independently of the other light sources illuminating the sensor.

A. Conventional Lock-in Detection
The principle of conventional lock-in detection is to multiply an electrical input signal by a reference signal defined as a pure sine wave locked to the frequency and phase of the modulated component to measure [1]. The resulting product includes components at various frequencies (sum and difference of the reference frequency with each frequency present in the signal). The only dc component remaining after the multiplication is the component of the signal at the exact reference frequency. A low-pass filter is used to remove all the alternating components and keep the dc component.
Commercially available lock-in amplifiers are typically limited to processing 32 channels in parallel, which is not sufficient to deal with CMOS or CCD array detectors.

B. Digital Lock-in Detection
To cope with the very high number of output signals of an array detector, a digital implementation of lock-in detection is possible [3]. It requires a fast array detector to acquire the output signals at least four times per modulation cycle using synchronous sampling. Digital lock-in detection has been used at low frequencies for many years in lock-in infrared thermography [4]. An efficient software for multichannel digital lock-in detection has recently been made available [5]. It relies on a  I  COMPARISON OF THE THREE APPROACHES TO LOCK-IN DETECTION computer-intensive algorithm and is not well adapted to perform lock-in detection in real time. Digital lock-in detection often requires storing the data acquired during the measurements in order to process them later.

C. Optical Lock-in Detection
Optical lock-in detection overcomes the requirements for fast array detectors, high memory capacity and computing power. The technique works in real time by applying in-phase and quadrature modulation to the optical input signal itself using optical modulators driven by a reference electrical signal. In optical lock-in detection, low pass filtering is physically performed by the accumulation of electrical charges in the pixels during the integration time of the array detector.
An early version of optical lock-in detection was described in 2002 [6] to improve interferometric microscopy techniques and optical coherence tomography. Since then, optical lock-in detection has also been used in phase cameras to achieve very sensitive sensing in the interferometric detection of gravitational waves [7].
In the field of optical spectroscopy, an optical lock-in spectrometer was described in [8]. Based on a 2D array detector and an acousto-optic deflector, it was used to perform time-resolved absorption measurements of quantum dots and nanocrystals excited by a modulated near-infrared diode laser. This approach of lock-in detection still required a complex digital processing of the images delivered by the 2D array detector. Table I compares the main features of the three different approaches to lock-in detection.

A. Overview
The optical lock-in spectrometer described in this article is based on a new instrumental concept using two identical compact array spectrometers synchronized in phase quadrature thanks to optical modulators. This concept is illustrated in Fig. 1. With this design, no signal processing is necessary to provide the in-phase and quadrature components, as shown in the next section.

B. Principle of Operation
A polychromatic optical beam is supposed to include temporally modulated spectral components. The corresponding optical signal S(t, λ) is the sum of a steady-state spectral distribution S dc (λ) and a periodic spectral distribution that can be expanded into a Fourier series, giving the following expression: where f is the fundamental modulation frequency, n is the harmonic order, S n (λ) and ϕ n (λ) respectively are the modulation amplitude and phase spectral components of the optical signal at wavelength λ and temporal frequency n × f.
The principle of the optical lock-in spectrometer is to measure the optical signal using two identical compact array spectrometers whose optical entrance ports are both amplitude-modulated at frequency f. The first spectrometer is modulated in phase and the second spectrometer is modulated in phase quadrature. The respective transmission functions at the entrance port of the in-phase and quadrature spectrometers can be modeled by the following equations: The resulting optical signals at the entrance of the in-phase and quadrature spectrometers are the products of the input signal by the respective transmission functions. If the integration time of the spectrometers is much longer than a modulation period, the process of charge accumulation in the pixels of the array detector acts as a low pass filtering stage eliminating the ac components, thereby delivering the following time-averaged spectral distributions: Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. Equations (4), (5) show that the dc spectral distribution must be compensated to determine the modulation amplitude and phase spectra. A third identical spectrometer could be added to the setup to measure the dc spectral distribution. The association of four identical spectrometers in a four-phase scheme would also be possible [3]. The dc-compensation method described here only relies on the in-phase and quadrature spectrometer. It consists in desynchronizing the optical modulators with respect to the reference signal. In doing so, all the periodic spectral components cancel out after the integration time, yielding a direct measurement of the dc spectral distribution. After this asynchronous measurement, the respective outputs of the spectrometers can be dc-corrected to provide the in-phase and quadrature spectral distributions I 1 (λ) and Q 1 (λ): The in-phase and quadrature spectral distributions can be combined to give the expressions of the modulation amplitude and phase spectra: The numerical application of (8), (9) is the only calculation involved in the optical lock-in spectrometer. No storage of timedomain data nor signal processing are necessary.

IV. EXPERIMENTAL SETUP
An implementation of the scheme depicted in Fig. 1 has been realized with standard fiber optic components. The setup is illustrated in Fig. 2. The polychromatic beam to analyze is collected using an optical system adapted to the type of measurement to perform (telescope for spectral radiance, integrating sphere for spectral radiant flux, cosine diffuser for spectral irradiance, etc.). The collection optics is connected to a multimode optical fiber and a fiber splitter (Y-bifurcated multimode optical fiber) is used to produce two identical guided beams. The in-phase and quadrature modulators are incorporated in a single unit based on an optical chopper (Thorlabs MC2000) and four optical ports, each consisting in a 90°off-axis parabolic collimator (Thorlabs RC08SMA). The unit was designed to produce well-collimated beams with a diameter comparable to the size of the chopper blade openings. The collimators were placed in quadrature arrangement: when one path is open or closed by the blade, the other path is half-open. A schematic view of the modulation unit is shown in Fig. 3. The transmission functions, also shown in Fig. 3, were measured using photodiodes. They are close to pure sine and cosine waves.
The resulting modulated optical signals are sent to two identical compact array spectrometers (Ocean Insight FX with Hamamatsu S11639-01 linear silicon CMOS array detector with 2048 pixels).
This optical lock-in spectrometer uses a periodic analog electrical signal as a reference. The analog signal is converted to TTL to drive the phase-locked loop (PLL) unit of the optical chopper. The electronic design of the analog-to-TTL converter is described in [3].
The absolute calibration of the two spectrometers was carried out using a calibrated tunable LED light source (Gamma Scientific RS7) traceable to NIST spectral radiance standards. Each spectrometer was calibrated with the modulation unit in operation at an arbitrary frequency. During the calibration of the spectrometers, their respective readings were adjusted to half the reference spectral irradiance of the calibrated LED light source. The calibration of the spectrometers was done using the same integration time than the one used in the lock-in mode.
The spectrometers were controlled in real-time by the software provided by the manufacturer. The calibration stage and lock-in data acquisition were automated with the graphical interface of the software.

V. APPLICATION EXAMPLE
An application example is presented to illustrate the benefits of using the optical lock-in spectrometer to perform spectral, color and photometric measurements in a real use case.
Here, the objective is to separate and measure several optical signals, each having a wide spectral power distribution, on top of an intense optical background, also having a wide spectral distribution. This case is typical of measurements of lighting sources performed indoors or outdoors in the presence of residual daylight, skyglow and undesirable contributions such as luminous signs, billboards, and other types of obtrusive light.
In the field of lighting, spectroradiometers are used to characterize lighting installations by measuring spectral irradiance, spectral radiance, illuminance, luminance, color rendering indices, chromaticity coordinates and correlated color temperature. Besides, the light sources themselves (lamps, luminaires, LED modules) are subject to regional or national regulations at the product level. For instance, the EU eco-design regulation UE 2019/2020 [9] includes mandatory requirements on chromaticity coordinates and color rendering that can be checked using spectroradiometers and other optical equipment. This UE regulation also imposes limits on flicker and the stroboscopic effect, two phenomena associated with temporal light modulation (TLM). In fact, the vast majority of lamps and luminaires connected to the mains power supply exhibit a residual level of TLM resulting from an imperfect rectifying of the ac current or from using pulse width modulation (PWM) to control the brightness level. In this experiment, the lock-in approach takes advantage of TLM levels below the visibility threshold.
The experimental setup is depicted in Fig. 4. It consists in three consumer lamps placed at approximately 1.2 m from an irradiance measurement head (cosine diffuser) connected to the optical lock-in spectrometer. The first lamp is a dc-powered incandescent lamp. It is placed closer to the sensor to generate an intense background having a wide spectral power distribution. The second lamp is a tunable LED lamp which is set to emit green light at a relative intensity level of about 50%. The intensity adjustment relies on a built-in PWM driver operating at 486 Hz. The third lamp is a white LED lamp exhibiting TLM at 100 Hz, originating from the rectified 50 Hz mains. The characteristics of the light sources are listed in Table II.  The spectral irradiance of the LED lamps was separately measured by using the optical lock-in spectrometer in the asynchronous mode. The results are shown in Fig. 5. The spectral irradiance given by the three lamps operating together was also measured in this mode to illustrate the superposition of the different light sources (Fig. 6). The settings and configuration of the two identical compact array spectrometers are given in Table III.
The numerical integration of the spectral irradiance values in the visible range gave irradiance and illuminance values, also reported in Table II. The irradiance given by the white LED lamp and the green LED lamp were respectively 26 times and 7 times less than the total irradiance of the three lamps operating together.
The reference signal was provided by a remote sensing assembly made of a small Newtonian telescope (Celestron 21024, 300 mm focal length, 76 mm aperture) equipped with a silicon  photodiode (Thorlabs SM05PD3A) placed at the focus of the spherical mirror, instead of the eyepiece, and connected to a transimpedance amplifier (Thorlabs PDA200). The photodiode and transimpedance amplifier are dc-coupled to be able to measure the ac and dc components of the waveform, after correcting for the dark current. The characteristics of the waveforms are given in Table IV. The remote sensing device has a narrow field of view of about 0.5°, allowing the experimenter to select the light source of interest by aiming in its direction to get an output signal proportional to the luminance waveform of the light source of interest. No stray light from the other lamps was detected by the telescope. The graphs of Fig. 7 show the luminance waveforms measured on the two LED lamps. Successive lock-in measurements were carried out by aiming the telescope respectively towards the white LED lamp and towards the green LED lamp. The results are shown in Fig. 8. For each LED lamp, the lock-in measurements successfully rejected the background signals of the other lamps.     9 shows the spectral distribution of the modulation amplitude of the green LED, compared with its spectral irradiance. The two spectral distributions are nearly identical, but they do not have the same absolute magnitude. The scaling factor between the two distributions corresponds to the modulation depth of the first Fourier component of the temporal waveform.
As shown in Fig. 10, a high noise level can be seen in the modulation amplitude spectrum of the white LED lamp. Because of the low modulation depth of this light source, the modulation amplitude spectrum is about 5 times smaller than its spectral irradiance and 30 times smaller than the total spectral irradiance given by the three lamps. Despite the noise level, the modulation The signal to noise ratio could be improved by increasing the number of averages used by the spectrometer, at the expense of a longer acquisition time.
The modulation amplitude spectrum of the white LED lamp was used to determine the following standard color parameters: correlated color temperature (CCT), chromaticity coordinates x and y, color rendering index Ra. Such parameters are calculated using integrals of the spectral distribution. Therefore, they are relatively insensitive to noise in the spectral data. The results show a very good agreement with the color parameters estimated from the single measurements carried out without the background illumination. For the green LED, the lock-in measurement also gave very consistent chromaticity coordinates in comparison with the measurement performed without background illumination. The measured color parameters are listed in Table V. As explained in Section III, the optical lock-in spectrometer measures the spectral distribution of the Fourier coefficient S 1 (λ)of the optical signal. It is possible to determine the steadystate irradiance and illuminance (dc values) of a given lamp by dividing the lock-in data by a scaling factor defined as the ratio between the lock-in modulation amplitude spectrum and the dc spectral irradiance. Generally speaking, this ratio should depend on the wavelength. However, a previous study of the spectral features of temporal light modulation in several technologies of light sources [10] showed that the modulation amplitude of LEDs at modulation frequencies of about 100 Hz is spectrally uniform, unlike fluorescent lamps and incandescent lamps which exhibit different modulation depths according to the wavelength.
Under the assumption of a uniform modulation depth across the visible spectral range, the scaling factor is a constant equal to the modulation depth mod 1 of the first Fourier component of the temporal waveform w(t). It is defined by the following equation: where w dc is the dc component of the temporal waveform, a 1 and b 1 are the Fourier coefficients of w(t) calculated using their mathematical definition in the time domain over a modulation The integrals of (11), (12) were computed numerically (discrete sum using a uniform time increment) for the two waveforms measured by remote sensing and shown in Fig. 7. The mod 1 factor was then calculated using (10). The numerical values are reported in Table VI. Using this ac-to-dc scaling factor, the irradiance and illuminance dc values were estimated from the modulated irradiance and illuminance values.
The estimated dc values lie within −13% to 9% of the respective values measured individually without lock-in detection. These measurements combine the uncertainties due to the noise in the waveform (uncertainty in the Fourier coefficients and in the dc value), and due to the noise in the lock-in spectral data. From a metrology point of view, it would be necessary to make more accurate temporal waveform measurements and spectral measurements to reduce the uncertainty associated with these indirect measurements of the absolute irradiance and illuminance.

VI. CONCLUSION
In this article, we demonstrated a new concept of optical lock-in spectrometer based on two identical fiber-optic compact array spectrometers associated with an optical modulator and a synchronization circuit. This approach enables the measurement of the spectral distribution of a modulated polychromatic optical beam while rejecting large backgrounds. Using this principle, an instrument was built and operated using standard off-the-shelf fiber-optic components.
The optical lock-in spectrometer was applied to a typical use case in the field of lighting measurement. The objective was to characterize the spectral irradiance and color parameters of two consumer LED lamps operating together on top of an intense luminous background. Here, lock-in detection was made possible by the periodic residual temporal light modulation exhibited by the two LED lamps at two different frequencies. In our experiment, the temporal luminous waveform was optically detected by a remote sensing device consisting in a small telescope and a photodiode. By aiming the telescope at the selected lamp, its luminous temporal waveform was detected and sent to the reference input of optical lock-in spectrometer. The results showed that the spectral power distribution of each LED lamp was accurately retrieved and the background (up to 30 times greater than the weakest signal) was rejected.
The lock-in modulation amplitude spectra were used to determine color parameters with excellent agreement with data measured individually in the conventional unlocked manner without background light. The ratio between the Fourier amplitude of the temporal waveform and its dc value provided a scaling factor allowing the absolute irradiance and illuminance of each LED lamp to be measured in the presence of the background lights. The deviations between the illuminance and irradiance measurements carried out with and without background lights were between −13% and 9%. The uncertainty associated with these measurements could be reduced by increasing the measurement time and taking more averages in the data acquisition procedure.
In this article, the intrinsic temporal light modulation of LED lamps acted as an optical footprint left by their power supply. This "signature" was detected by remote sensing, without any contact with the light sources or their power supply. Once the temporal waveform was detected, a reference signal could be provided to the optical lock-in spectrometer for its successful operation. This principle opens interesting opportunities in remote sensing to perform spectroradiometric measurements of obtrusive lights generated by a given luminaire on sites where background lights are often a source of perturbations and errors.
Other applications are foreseen in physical and chemical analytical equipment relying on compact array spectrometers. For instance, lock-in backscattering spectral reflectance measurements could be useful to reject background light and differentiate reflected signals from signals produced by the fluorescence of the sample under test. Differential optical absorption spectrometry (DOAS) long-path measurements of urban air pollutants could also benefit from a lock-in approach. In absorption and Raman spectrometry, the optical lock-in approach could be implemented with modulated excitation beams to provide more accurate results. Photothermal techniques such as multi-wavelengths radiation thermometry and laser absorption radiation thermometry could also incorporate an optical lock-in spectrometer to provide more wavelength data without compromising the measurement time.