CN107228684B - PSD output useful signal extraction method based on autocorrelation filtering technology - Google Patents
PSD output useful signal extraction method based on autocorrelation filtering technology Download PDFInfo
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- CN107228684B CN107228684B CN201710466661.7A CN201710466661A CN107228684B CN 107228684 B CN107228684 B CN 107228684B CN 201710466661 A CN201710466661 A CN 201710466661A CN 107228684 B CN107228684 B CN 107228684B
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Abstract
a PSD output useful signal extraction method based on an autocorrelation filtering technology relates to the field of photoelectric detection, and solves the problems that the correlation degree of noise at a high level and the noise at a low level in the existing sampling and holding method is low, and the noise reduction effect is limited, and the problem that the same frequency of a reference signal and an optical pulse signal is difficult to ensure in a cross-correlation method. The invention carries out autocorrelation operation on PSD output signals, removes noise caused by stray light and the like by utilizing the same-frequency correlation and different-frequency uncorrelated properties of autocorrelation, reserves the same-frequency components of PSD output and reference signals, filters fundamental wave signals from the result of the autocorrelation operation by a band-pass filter, carries out amplitude extraction on the fundamental wave signals, and takes the extracted amplitude as the metric value of PSD output useful signals. The method realizes the removal of noise generated by stray light and the extraction of a PSD output useful signal, and improves the accuracy of signal extraction.
Description
Technical Field
the invention relates to the field of photoelectric detection, in particular to a method for extracting useful signals output by a Position Sensitive Detector (PSD) based on an autocorrelation filtering technology, and aims to improve the position accuracy of a PSD detection light spot.
Background
The PSD is used as a high-precision photoelectric position sensitive detector, and is easily interfered by factors such as background light and the like to cause errors in the detection of the position of a light spot on a photosensitive surface of the PSD. In order to reduce the influence of background light and other factors, the current methods mainly include a sample-and-hold method and a cross-correlation method. Both methods are premised on the modulation of a light beam incident on the photosensitive surface of the PSD into an optical pulse signal of a specific frequency.
in the conventional patent document, although the publication number is 104215265a, which is named "a high-precision PSD signal noise reduction method" in which a signal at a high level and a signal at a low level are sampled and held in a PSD, and then the two signals are subjected to a difference operation to reduce noise, the noise reduction effect of the sample-and-hold method is limited because the correlation between the noise at the high level and the noise at the low level is generally low.
useful signals output by the PSD are extracted by using a cross-correlation method (for example, in research on straightness measuring system of long guide rail based on 2D-PSD, the university of Chongqing Master academic thesis 2015), and the same frequency of the reference signals and the optical pulses is required to be ensured. One is to directly take a signal from an optical pulse signal as a reference signal, and the disadvantage is that when the optical beam modulation circuit and the PSD output signal demodulation circuit are far away, a long cable is required, which is inconvenient; another situation is that when the use site does not allow the use of a long cable, the reference signal is generated in the demodulation circuit by the self-generating circuit, which has a disadvantage that it is difficult to ensure the reference signal to be the same frequency as the optical pulse signal when the frequency of the optical pulse signal is unstable. Therefore, a method for extracting a useful signal output by a PSD (phase-sensitive detector) based on an autocorrelation filtering technology is provided, which is used for solving the problems that the noise reduction effect in the current sample-and-hold method is limited and the same frequency of a reference signal and an optical pulse signal is difficult to ensure in a cross-correlation method, and simultaneously improving the precision of signal extraction.
disclosure of Invention
in order to solve the above problems, a method for extracting a useful signal from a PSD based on an autocorrelation filtering technique is proposed. The method comprises the steps of carrying out autocorrelation operation on a PSD output signal, removing noise caused by stray light and the like by utilizing the same-frequency correlation and different-frequency uncorrelated properties of autocorrelation, retaining the same-frequency components of the PSD output and a reference signal, filtering a fundamental wave signal from a result of the autocorrelation operation through a band-pass filter, carrying out amplitude extraction on the fundamental wave signal, and taking the extracted amplitude as a metric value of a useful signal output by the PSD.
A method for extracting a useful signal output by a PSD (phase-sensitive detector) based on an autocorrelation filtering technology comprises the following steps:
1) The self-correlation operation is used for removing noise generated by the alternating current component of the stray light signal in the PSD output signal;
let the optical pulse signal incident on the PSD be:
in formula (1): a is the amplitude of the optical pulse signal x (t), t is time, W is the pulse width of the optical pulse signal, and omega 0 is the modulation angular frequency of the optical pulse signal.
let the parasitic light signal n (t) incident on the PSD be expressed as:
n(t)＝n+n(t) (2)
in formula (2): nD represents the DC component of the stray light signal, and nA (t) represents the AC component of the stray light signal.
x (t) and n (t) are incident on the PSD photosurface, and the PSD generates output signals of:
y(t)＝x′(t)+n′(t) (3)
In formula (3): x '(t) is a useful signal caused by x (t), and n' (t) is noise caused by n (t).
x' (t) is expressed as:
In formula (4): k is the response sensitivity of the PSD.
n' (t) is expressed as:
n′(t)＝n′+n′(t) (5)
in formula (5): n 'a (t) represents an alternating current component of PSD output noise caused by the stray light signal, and n' D represents a direct current component of PSD output noise caused by the stray light signal.
y (t) the autocorrelation operation is:
In formula (6): τ is the time delay of the signal.
since n' a (t) is an alternating component of PSD output noise, and has a random property, it can be known from the correlation operation property that:
formula (7) is substituted for formula (6) to obtain:
in formula (8): and B ═ KA is the amplitude of the useful signal x' (t).
From equation (8), even if the angular frequency ω 0 of the pulse signal x (t) varies unstably, the autocorrelation operation can effectively remove the ac component of the PSD output noise while retaining the useful signal.
2) the band-pass filtering is used for filtering direct-current components and multiple harmonics of PSD output noise and filtering fundamental wave components of an autocorrelation result;
The Fourier series expansion of x' (t) is:
substituting formula (9) for formula (8) to obtain:
the fourier transform of equation (10):
in formula (11): δ (ω), δ (ω + n ω 0), and δ (ω -n ω 0) represent unit pulse functions.
The transfer function of the bandpass filter used is:
In formula (12): Δ ω 0 < ω 0.
band-pass filtering Ry (τ), i.e., multiplying equation (11) by equation (12):
equation (13) performs an inverse fourier transform to obtain:
as shown in equation (14), the band-pass filtered signal z (τ) contains no noise or multiple harmonics due to stray light, only the fundamental wave, and retains the incident light pulse information.
3) Extracting amplitude characteristics, namely extracting the amplitude of a useful signal;
The amplitude of the extraction equation (14) is:
known from formula (15): the amplitude Az is determined only by the optical pulse signal amplitude a, the pulse width W and the angular frequency ω 0. The amplitude Az is used as a measure of the PSD output useful signal.
Has the advantages that: the method solves the problems that the noise reduction effect is limited in the sampling and holding method and the same frequency of the reference signal and the optical pulse signal is difficult to ensure in the cross-correlation method, realizes the removal of noise generated by stray light, extracts a useful signal output by the PSD, and improves the accuracy of signal extraction.
Drawings
FIG. 1 is a schematic diagram of the autocorrelation signal extraction of the present invention;
fig. 2 is a diagram illustrating the effect of the autocorrelation signal extraction of the present invention.
Detailed Description
the following detailed description of the embodiments of the present invention will be made with reference to the accompanying drawings 1:
1) the self-correlation operation is used for filtering noise generated by the alternating current component of the stray light signal in the PSD output signal;
the optical pulse signals incident on the PSD are:
in formula (16): the amplitude a of the signal is 5, the angular frequency ω 0 is 0.01 pi, and the pulse width W is 60.
the stray light signal is:
n(t)＝n+n(t) (17)
in formula (17): the ac component na (t) of the noise satisfies the dc component nD of 0.5.
The response sensitivity K of the PSD is 0.2, and x (t) and n (t) are incident on the PSD surface. The output signal generated by the PSD is:
y(t)＝x′(t)+n′(t) (18)
In formula (18): x '(t) is a useful signal caused by x (t), and n' (t) is noise caused by n (t).
x' (t) is expressed as:
n' (t) is expressed as:
n′(t)＝n′+n′(t) (20)
In formula (20): n' A (t) satisfies an AC component representing PSD output noise caused by the stray light signal,
n′＝Kn＝0.1 (21)
in formula (21): n' D represents the direct current component of PSD output noise caused by stray light signals;
y (t) the autocorrelation operation is:
in formula (22): τ is the time delay of the signal.
since n' a (t) is an alternating component of PSD output noise, and has a random property, it can be known from the correlation operation property that:
formula (23) is substituted for formula (22):
2) The band-pass filter is used for filtering direct-current components and multiple harmonics of PSD output noise and filtering fundamental wave components;
the Fourier expansion of x' (t) is:
The formula (25) substitutes the formula (24) to perform autocorrelation calculation to obtain the autocorrelation calculation result of y (t):
the Fourier transform of equation (26):
In formula (27): δ (ω), δ (ω +0.01n π) and δ (ω -0.01n π) represent unit pulse functions.
the transfer function of the bandpass filter used is:
band-pass filtering Ry (τ), i.e., multiplying equation (27) by equation (28):
Inverse fourier transform equation (29) yields:
z(τ)＝0.13cos(0.01πτ) (30)
as shown in equation (30), the band-pass filtered signal z (τ) contains no noise and multiple harmonics due to stray light, only the fundamental wave, and retains the incident light pulse information.
3) Extracting amplitude characteristics, namely extracting the amplitude of a useful signal;
Amplitude extraction is performed on the fundamental wave signal formula (30), so that Az is 0.13, and the Az is used as a measurement value of a PSD output useful signal.
Claims (1)
1. a PSD output useful signal extraction method based on an autocorrelation filtering technology is characterized by comprising the following steps:
1) the self-correlation operation is used for removing noise generated by the alternating current component of the stray light signal in the PSD output signal;
let the optical pulse signal incident on the PSD be:
in formula (1): a is the amplitude of the optical pulse signal x (t), t is time, W is the pulse width of the optical pulse signal, and omega 0 is the modulation angular frequency of the optical pulse signal;
let the parasitic light signal n (t) incident on the PSD be expressed as:
n(t)＝n+n(t) (2)
in formula (2): nD represents the DC component of the stray light signal, nA (t) represents the AC component of the stray light signal;
x (t) and n (t) are incident on the PSD photosurface, and the PSD generates output signals of:
y(t)＝x′(t)+n′(t) (3)
in formula (3): x '(t) is useful signal caused by x (t), n' (t) is noise caused by n (t);
x' (t) is expressed as:
In formula (4): k is the response sensitivity of the PSD;
n' (t) is expressed as:
n′(t)＝n′+n′(t) (5)
in formula (5): n 'a (t) represents an alternating current component of PSD output noise caused by the stray light signal, and n' D represents a direct current component of PSD output noise caused by the stray light signal;
y (t) the autocorrelation operation is:
In formula (6): tau is the time delay of the signal;
since n' a (t) is an alternating component of PSD output noise, and has a random property, it can be known from the correlation operation property that:
formula (7) is substituted for formula (6) to obtain:
in formula (8): and B ═ KA is the amplitude of the useful signal x' (t).
as shown in equation (8), even if the angular frequency ω 0 of the pulse signal x (t) varies unstably, the autocorrelation operation can effectively remove the ac component of the PSD output noise while retaining the useful signal;
2) the band-pass filtering is used for filtering direct-current components and multiple harmonics of PSD output noise and filtering fundamental wave components of an autocorrelation result;
the Fourier series expansion of x' (t) is:
substituting formula (9) for formula (8) to obtain:
The fourier transform of equation (10):
In formula (11): δ (ω), δ (ω + n ω 0), and δ (ω -n ω 0) represent unit pulse functions;
the transfer function of the bandpass filter used is:
in formula (12): Δ ω 0 < ω 0;
band-pass filtering Ry (τ), i.e., multiplying equation (11) by equation (12):
equation (13) performs an inverse fourier transform to obtain:
as shown in the formula (14), the band-pass filtered signal z (τ) does not contain noise and multiple harmonics caused by stray light, only contains fundamental waves, and retains the pulse information of incident light;
3) extracting amplitude characteristics, namely extracting the amplitude of a useful signal;
the amplitude of the extraction equation (14) is:
known from formula (15): the amplitude Az is only determined by the amplitude A, the pulse width W and the angular frequency omega 0 of the optical pulse signal; the amplitude Az is used as a measure of the PSD output useful signal.
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