Research on the application of lock-in amplifier in noise resistance test system

The main function of the laser smoke attenuation test system is to measure the transmission performance of infrared laser (1.06um and 10.6um) in special smoke. When working, the transmitting system emits infrared laser, transmits it for a distance in the atmosphere, and releases special smoke on its optical path. The test system tests the intensity change of the laser when it reaches the receiving system through the smoke. Since there are various infrared radiation sources in nature (reflection of light by objects, radiation from objects themselves, radiation from the surrounding environment, etc.), their intensity is sometimes even stronger than the signal. Therefore, during the measurement process, strong background radiation will inevitably enter the test system, forming the so-called background noise; in addition, the interference of atmospheric turbulence to infrared laser radiation cannot be ignored. How to effectively remove the influence of noise and obtain the high-precision data we expect is the main problem we face. The strong anti-noise ability of the lock-in amplifier enables this problem to be well solved. This article will discuss and study the functional characteristics of the lock-in amplifier and its application method in the laser smoke test system. The 

noise problem existing in the smoke attenuation test system 

There are many interference factors in the laser smoke attenuation test system. In nature, the sun, moon, stars, and the ground are all natural infrared radiation sources. When conducting field tests (outdoor tests), the radiation from natural radiation sources will interfere with the work of infrared instruments and have a great impact on the test results of the system. This interference can be called background radiation interference. When the infrared system is measuring in the field, the strong background radiation caused by natural radiation sources will inevitably enter the system. These radiations become DC background signals after photoelectric conversion, and their intensity is sometimes even several orders of magnitude greater than the useful signal. If the DC amplification method is used directly to measure infrared radiation, it will cause a large error code. 

In view of this situation, the traditional infrared system often uses the conversion method, that is, modulating the infrared radiation into an AC signal and then transmitting it. We can use a modulator (chopper) to complete this task. The modulator converts the DC radiation signal into an AC signal, which can be amplified by an AC amplifier or related detection instruments to weaken the DC drift and DC background. However, this method can only roughly remove the DC component in the background noise, but it is powerless against the background radiation interference close to the modulation frequency of the modulation disk, especially when the intensity of the background radiation interference is much greater than the measured infrared radiation intensity. Therefore, we must find a way to remove this interference. The 

working principle and composition of the lock-in amplifier 

Synchronous coherent detection technology has developed rapidly in the past 20 years. It is an important means to extract weak signals from strong noise. It has been increasingly widely used in various disciplines, especially in the field of electronics. Information theory and random process theory are its main theoretical basis, and the main contents include correlation function and correlation reception (also known as correlation detection). This technology uses the characteristics of signal periodicity and noise randomness, that is, the signal and noise are unrelated to each other, and through correlation operations (autocorrelation or cross-correlation), the purpose of noise removal is achieved. 

Correlation detection principle 
The correlation detection principle is shown in the figure:

Figure 1 Schematic diagram of cross-correlation detection 

In the figure, f1(t) is the input signal at the receiving end, f2(t) is the local signal, whose repetition period is the same as the repetition period of s1(t) in the input signal and is "clean", and n1(t) is the noise signal. 

Assume that the input signal is: 
f1(t)= s1(t)+n1(t) and 
the local signal is: 
f2(t)=s2(t). 
Then its correlation function  is:

In the above formula, τ is the time interval between the two points under study, that is, the time delay between the two signals. 

Since the signal and the random noise occur independently, their cross-correlation function will be a constant, which is equal to the product of the average values ​​of the two random functions. If one of the average values ​​is zero, the correlation function is zero. Since the noise average value is zero, Rns2(τ) in the above formula is zero. Therefore, the output of the correlation function is only the correlation result between the signal and the local signal, and the noise is removed. In practical applications, only when the time for calculating the average value of the correlation function is relatively long, Rns2 
(τ) is close to zero, thereby obtaining a higher output signal-to-noise ratio. This time can be determined by experiment. Generally, its value is 4-5 times the time constant RC value of the low-pass filter used by the integrator. 

From the above simple formula, we can see that the cross-correlation operation can indeed greatly remove the influence of noise. The lock-in amplifier is a synchronous coherent detector designed using the cross-correlation principle. It is an electronic device that performs correlation operations on the measured signal and the reference signal. It has a very narrow signal and noise bandwidth. According to the meaning of the Q value of the usual bandpass filter, its equivalent Q value can reach the order of 108, which is unattainable by conventional filters. 

The composition and 
structure of the lock-in amplifier are briefly described below. A typical lock-in amplifier is shown in Figure 2. As can be seen from Figure 2, a general lock-in amplifier can be divided into three parts, namely: signal channel, reference channel and correlator (there should also be a DC amplifier behind the integrator, which is not shown in the figure). The following introduces their respective functions and components: 

Correlator 
The correlator is a key component of the lock-in amplifier, including two parts, a multiplier and an integrator. It finally completes the cross-correlation function operation between the measured signal and the reference signal. It must have the characteristics of large dynamic range, small drift, adjustable time constant, stable gain and wide frequency range. It requires the input signal to be a sine wave or square wave. If the measured signal is a DC signal, a chopper can be used to convert it into an AC square wave before conversion detection.

Figure 2 Schematic diagram of the structure of the lock-in amplifier 

Signal channel 
The signal channel is located before the correlator and consists of an input amplifier, a low-noise preamplifier, various active filters and amplifiers. Its function is to amplify weak signals to a level sufficient to drive the correlator, and it also has the function of suppressing and filtering out some noise and interference, expanding the dynamic range of the instrument. The optimal signal source resistance of its preamplifier must be able to match the noise with different sensors to obtain the best noise characteristics. The 

reference channel 
is used to output a symmetrical square wave with a certain amplitude and a duty cycle of 1:1 that is synchronized with the input signal to drive the correlator. It consists of a trigger circuit, a frequency multiplication circuit, a phase shift circuit, a square wave generation and a drive circuit. 

DC amplifier 
This is also an important part of the lock-in amplifier, which is not drawn in the figure. Its main function is to amplify the DC or slow-changing signal output by the integrator so that it meets the signal requirements of the subsequent data acquisition system. The main problem of the DC amplifier is the influence of zero drift. Considering that the output of the pre-stage correlator may be very small, a low-drift operational amplifier should be selected as the pre-stage of the DC amplifier, and at the same time, the 1/f noise should be as small as possible. 

The composition of the laser smoke attenuation test system and the application of the lock-in amplifier 

The composition of the laser smoke attenuation test system 
The infrared system is essentially an optical-electronic system. Its basic function is to convert the received infrared radiation into an electrical signal and use it to achieve a certain practical application purpose. The laser smoke attenuation test system is a typical infrared system, and therefore has the characteristics of a general infrared system: it includes an optical system, a modulation disk, an infrared detector, an electronic circuit, and a display and recording device. The continuous infrared radiation modulation disk modulates the alternating signal output, which is attenuated during the transmission process by the selective absorption of certain gas molecules in the atmosphere and the scattering of suspended particles (aerosol) in the infrared smoke. The attenuated infrared radiation is received by the optical system and focused on the infrared detector response plane. The infrared detector converts the infrared radiation into telecommunication for final analysis and processing. This is the working principle of the laser smoke attenuation test system. 

As mentioned above, the structural diagram of this system is shown in Figure 3 (only the receiving part is drawn here).

Figure 3 Schematic diagram of the receiving part of the laser smoke attenuation test system 

As can be seen from Figure 3, the lock-in amplifier can be used in the signal conditioning circuit behind the detector to remove noise from the electrical signal reflecting the laser intensity transmitted by the detector, and then send the signal to the next-level data acquisition system for interpretation and analysis. Its working process is as follows: the infrared laser signal and the infrared background noise pass through the aperture together, and are modulated by the optical modulation disk to become an AC square wave signal, and then are projected onto the photosensitive surface of the infrared detector through the optical system. The detector outputs a sinusoidal AC signal that has a certain relationship with the laser intensity and is sent to the lock-in amplifier for measurement. The measured result will be processed by the signal conditioning circuit and sent to the next-level data acquisition system for recording and analysis. The reference signal of the correlation amplifier is given by the oscillation source that controls the optical modulation disk. As can be seen from the figure, the correlation amplifier plays a connecting role in this system and is very important. 

Several issues that need to be noted in the actual application of the lock-in amplifier 
should be explained here: Although the lock-in amplifier has many advantages, it has several issues that need to be noted in the actual application process. The measurement time of the correlation demodulator and its influence on the measurement results The integration operation of the correlation demodulator shown in Figure 1 is generally implemented by using an RC low-pass filter, which is equivalent to an integrator with a time constant of 3RC-5RC. Therefore, the integration time of the correlation demodulator cannot be infinite (it is impossible for any signal to have an infinite measurement time). Obviously, the cross-correlation operation within a finite time cannot completely remove the noise. If allowed, the longer the measurement time, the smaller the signal that can be detected. 

Acquisition of reference signal 
The correlator is a key component of the lock-in amplifier. When performing correlation operations, there must be a square wave reference signal with a constant amplitude and the same frequency as the signal. In many applications of lock-in amplifiers, this reference signal can be obtained from an oscillator (as shown in the figure), and then the measured signal also has this frequency, so that the same frequency requirement is achieved, and then the amplitude of the sinusoidal signal in the observation noise can be detected. Generally speaking, commercial choppers have reference signal outputs available for use. In addition, its amplitude should usually be greater than 100mV. 

The phase of the reference signal 
cannot be known in advance when detecting the phase of the measured signal. Therefore, a phase shift circuit of the reference signal must be set in the correlation demodulator to adjust the phase to be the same as or opposite to the measured signal. The change of phase should be able to be adjusted within the range of 0-360 degrees. 

The improvement degree of the signal-to-noise ratio of the lock-in amplifier 
The improvement degree of the signal-to-noise ratio of the lock-in amplifier is SNIR=2Bin/△fn, Bin is the bandwidth of the bandpass filter in front of the correlation demodulator, and △fn is the noise bandwidth of the low-pass filter. Since △fn is much smaller than Bin, the signal-to-noise ratio of the signal will be greatly improved. However, when the noise is too large, the nonlinear characteristics of the device make the multiplier no longer have the ideal multiplication characteristics and enter the overload state. At this time, the output signal-to-noise ratio of the correlation demodulator deteriorates rapidly. Therefore, when designing the application, the correlation demodulator should be made to have a large overload capacity as much as possible; In addition, if △fn is too small, the measurement time will be too long, so it should be recognized that the improvement degree of the signal-to-noise ratio of the correlation demodulator is limited. 

Conclusion 

From the above discussion, it can be seen that the modulation disk in the laser smoke attenuation test system changes the infrared laser radiation from DC radiation to alternating radiation, and its output reference signal can be directly used by the lock-in amplifier, thus fully meeting the two main conditions required by the lock-in amplifier in the application of this system. After the lock-in amplifier is applied, the measurement accuracy of the system is greatly improved, and the ability to resist background radiation interference is also greatly enhanced, providing a more accurate measurement method for the smoke research department to test various technical indicators of smoke.