Grating moire fringe signal linearization subdivision method

Abstract

The application discloses a grating Moiré fringe signal linearization subdivision method, which comprises the following steps: carrying out analog-digital conversion on the sine signal and the cosine signal output by a grating sensor to obtain a sine digital signal and a cosine digital signal; calculating an interval coding signal according to the sine digital signal and the cosine digital signal and a comparison operation, and constructing an approximate triangular wave signal; constructing a coefficient compensation signal according to the sine digital signal and the cosine digital signal; compensating the approximate triangular wave signal to obtain a triangular wave signal; and dividing the triangular wave signal into multiple intervals by using the interval coding signal, linearly combining the multiple intervals, and obtaining a sawtooth wave signal proportional to the grating displacement. Through the processing of the original sine and cosine signals, one period of Moiré fringe signals is divided into 16 intervals of approximate linear signals, and a compensation signal is simultaneously proposed, so that the linearity of the constructed linear signal is improved. The method only uses simple addition, subtraction, multiplication, division, absolute value and comparison operations, and can realize higher rate subdivision.

Description

Technical Field

[0001] This invention belongs to the field of optical signal processing technology, specifically relating to a method for linearizing and subdividing grating moiré fringe signals. Background Technology

[0002] The grating pitch, or the grating line density, is a crucial factor affecting the measurement accuracy of grating sensors. Increasing the number of lines can improve accuracy. However, a higher line count places higher demands on the manufacturing process and consumes more resources. Furthermore, a smaller grating pitch makes the optical and mechanical design of the entire measurement system more difficult, and also slows down the maximum grating movement speed, thus limiting the grating line density.

[0003] Currently, most grating sensors on the market have a grating pitch of 20 micrometers, which is far from meeting the requirements for high-precision measurement. Higher-precision grating sensors are difficult to manufacture and expensive, making mass production impossible. Subdivision can be achieved by dividing the electrical signal output by the grating sensor according to the amplitude, utilizing the correspondence between the amplitude of the moiré fringe signal and the grating displacement. An analog-to-digital converter (ADC) is used to convert the electrical signal output by the grating sensor into a digital quantity, and then a lookup table can be used to obtain the displacement value less than one grating pitch. When the subdivision number is high, the workload of creating the lookup table is large, requiring more processing system memory. Furthermore, due to the poor linearity of the sine wave waveform, especially near extreme points, the voltage amplitude does not change significantly with displacement, which can introduce large errors in the measurement results. To solve these problems, Chinese Patent CN113587963 discloses a subdivision method for moiré fringe signals. This method constructs a new signal function from a sine signal, a coarse signal, and a DC component, performing an eight-fold coarse subdivision of the signal within the period, and then further refining each interval within the eight-fold coarse subdivision. This solves the subdivision accuracy loss caused by the inherent accuracy problem of the ADC itself. However, the constructed signal linearity is not high, and the error is large in fine time-division subdivision. Application CN201710402058.2, entitled "A Method for Subdividing Grating Moiré Fringe," discloses a pre-linearization process for the original sine and cosine moiré fringe signals, employing a construction method based on the difference and sum of the absolute values ​​of the sine and cosines, and provides a corresponding real-time compensation function. However, to reduce the error caused by signal amplitude fluctuations, the compensation function is complex, and the final linearization degree is not high. Summary of the Invention

[0004] The purpose of this invention is to provide a linear subdivision method for grating moiré fringe signals, which solves the problems of low subdivision number and large error in grating signal amplitude segmentation subdivision.

[0005] The technical solution adopted in this invention is a linear subdivision method for grating moiré fringe signals, wherein the grating moiré fringe signals are sine and cosine signals, and is implemented according to the following steps:

[0006] Step 1: Convert the sine and cosine signals output by the grating sensor from analog to digital to obtain sine and cosine digital signals;

[0007] Step 2: Calculate the interval-coded signal based on the sine and cosine digital signals and the comparison operation, and construct an approximate triangular wave signal;

[0008] Step 3: Construct coefficient compensation signals based on the sine and cosine digital signals;

[0009] Step 4: Compensate the approximate triangular wave signal to obtain the triangular wave signal;

[0010] Step 5: Divide the triangular wave signal into multiple intervals using interval coding signals, and linearly combine the multiple intervals to obtain a sawtooth wave signal that is proportional to the grating displacement.

[0011] The process of calculating the interval-coded signal in step 2 is as follows: For the sinusoidal digital signal V... s (x) and cosine digital signal V c (x) Take the absolute value to obtain the absolute value of the sinusoidal digital signal |V s (x)|、Absolute value of cosine digital signal|V c (x)|; to respectively represent the sinusoidal digital signal V s (x) and cosine digital signal V c The comparison operation between (x) and 0 yields the sinusoidal interval encoded signal. Sum and cosine interval encoded signal

[0012] The absolute value of a sinusoidal digital signal |V s (x)|and the absolute value of the cosine digital signal|V c By comparing (x)|, the absolute value interval encoded signal is obtained.

[0013] Based on the absolute value of the sinusoidal digital signal |V s (x)|and the absolute value of the cosine digital signal|V c (x)|Construct the tangent signal

[0014] Construct the tangent signal based on the tangent signal V1(x)

[0015] By comparing two tangent signals, the tangent interval encoded signal is obtained.

[0016] sinusoidal interval encoded signal The cosine interval encoded signal bit1, the absolute value interval encoded signal bit2, and the tangent interval encoded signal bit3 are the interval encoded signals.

[0017] The specific process of constructing the approximate triangular wave signal in step 2 is as follows: construct the approximate triangular wave signal based on the tangent signal V1(x) and the tangent signal V2(x).

[0018] The expression for the coefficient compensation signal in step 3 is:

[0019] C(x) = 0.0102 × V3(x) 3 -0.0661×V3(x) 2 +0.0012×V3(x)+1.0547

[0020] Where C(x) represents the coefficient compensation signal and V3(x) represents the approximate triangular wave signal.

[0021] Step 4 is as follows: the approximate triangular wave signal is compensated by the coefficient compensation signal, and the expression is: V4(x)=V3(x)C(x);

[0022] Where V4(x) represents the triangular wave signal, V3(x) represents the approximate triangular wave signal, and C(x) represents the coefficient compensation signal.

[0023] In step 5, the amplitude of the sawtooth wave signal is linearly related to the grating displacement.

[0024] In step 1, the sine and cosine signals output by the grating sensor are converted from analog to digital in the analog-to-digital converter.

[0025] The beneficial effects of this invention are:

[0026] The linearization subdivision method for grating moiré fringe signals of this invention divides a one-cycle moiré fringe signal into approximately linear signals of 16 intervals by processing the original sine and cosine signals. It also introduces a compensation signal to improve the linearity of the constructed linear signals. This method uses only simple addition, subtraction, multiplication, division, absolute value, and comparison operations, enabling higher subdivision ratios. Attached Figure Description

[0027] Figure 1 This is a flowchart of the linearization and subdivision method for grating moiré fringe signals of the present invention;

[0028] Figure 2 This is a schematic diagram of the sine and cosine digital signals in Embodiment 3 of the present invention;

[0029] Figure 3This is a schematic diagram of the absolute values ​​of the sine and cosine digital signals in Embodiment 3 of the present invention;

[0030] Figure 4 This is a schematic diagram of the sine interval encoded signal bit0 and the cosine interval encoded signal bit1 obtained in Embodiment 3 of the present invention;

[0031] Figure 5 This is a schematic diagram of the absolute value interval encoded signal bit2 obtained in Embodiment 3 of the present invention;

[0032] Figure 6 This is a schematic diagram of constructing the tangent signal V1(x) in Embodiment 3 of the present invention;

[0033] Figure 7 This is a schematic diagram illustrating the construction of the tangent signal V2(x) based on the tangent signal V1(x) in Embodiment 3 of the present invention;

[0034] Figure 8 This is a schematic diagram of bit3 of the tangent interval encoded signal obtained in Embodiment 3 of the present invention;

[0035] Figure 9 This is a schematic diagram of constructing an approximate triangular wave signal V3(x) in Embodiment 3 of the present invention;

[0036] Figure 10 A schematic diagram illustrating the error e3(x) between the approximate triangular wave signal V3(x) and the standard linear signal in Embodiment 3 of the present invention;

[0037] Figure 11 This is a schematic diagram of the triangular wave signal V4(x) obtained in Embodiment 3 of the present invention;

[0038] Figure 12 This is a schematic diagram showing the error e4(x) between the triangular wave signal V4(x) and the standard linear signal obtained in Embodiment 3 of the present invention;

[0039] Figure 13 This is a schematic diagram of the combination of four interval encoded signals obtained in Embodiment 3 of the present invention;

[0040] Figure 14 This is a schematic diagram of the interval division result and the expression of the sawtooth wave signal V5(x) in Embodiment 3 of the present invention;

[0041] Figure 15 This is a schematic diagram of the sawtooth wave signal V5(x) obtained in Embodiment 3 of the present invention, which is proportional to the grating displacement. Detailed Implementation

[0042] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0043] Example 1

[0044] The present invention provides a method for linearizing and subdividing grating moiré fringe signals, such as... Figure 1 As shown, the grating moiré fringe signal is a sine signal and a cosine signal. The sine and cosine signals output by the grating sensor are converted from analog to digital to obtain sine and cosine digital signals. Based on the sine and cosine digital signals and comparison operations, the interval coded signal is calculated, and an approximate triangular wave signal is constructed. The coefficient compensation signal is constructed based on the sine and cosine digital signals. The approximate triangular wave signal is compensated to obtain the triangular wave signal. The triangular wave signal is divided into multiple intervals using the interval coded signal. The multiple intervals are linearly combined to obtain a sawtooth wave signal proportional to the grating displacement.

[0045] In this invention, displacement can be obtained by performing arctangent calculation on the sine and cosine signals output by the grating sensor. However, the sine and cosine signals change slowly near extreme points, and direct amplitude segmentation or arctangent calculation results in significant errors. This invention utilizes the good linearity of the tangent function near zero. By constructing tangent, cotangent, phase-shifted tangent, and phase-shifted cotangent signals, it transforms a one-cycle sine and cosine signal into an approximate triangular wave signal with 16 intervals within one cycle. The linearity is further improved through a compensation signal.

[0046] Example 2

[0047] The present invention provides a method for linearizing and subdividing grating moiré fringe signals, wherein the grating moiré fringe signals are sine and cosine signals, and is implemented according to the following steps:

[0048] Step 1: Convert the sine and cosine signals output by the grating sensor into analog and digital signals by an analog-to-digital converter to obtain sine and cosine digital signals. In this invention, since the analog signal output by the grating sensor is nonlinear, it is difficult to directly obtain the displacement. Therefore, it needs to be converted into a digital signal and the displacement is calculated by the processor.

[0049] Step 2: Calculate the interval-coded signal based on the sine and cosine digital signals and the comparison operation. The process of calculating the interval-coded signal is as follows: For the sine digital signal V... s (x) and cosine digital signal V c (x) Take the absolute value to obtain the absolute value of the sinusoidal digital signal |V s (x)|、Absolute value of cosine digital signal|V c (x)|; to respectively represent the sinusoidal digital signal V s (x) and cosine digital signal V c The comparison operation between (x) and 0 yields the sinusoidal interval encoded signal. Sum and cosine interval encoded signal

[0050] The absolute value of a sinusoidal digital signal |V s (x)|and the absolute value of the cosine digital signal|V c By comparing (x)|, the absolute value interval encoded signal is obtained.

[0051] Based on the absolute value of the sinusoidal digital signal |V s (x)|and the absolute value of the cosine digital signal|V c (x)|Construct the tangent signal

[0052] Construct the tangent signal based on the tangent signal V1(x)

[0053] By comparing two tangent signals, the tangent interval encoded signal is obtained.

[0054] sinusoidal interval encoded signal The cosine interval encoded signal bit1, the absolute value interval encoded signal bit2, and the tangent interval encoded signal bit3 are the interval encoded signals.

[0055] Constructing an approximate triangular wave signal: Based on the tangent signals V1(x) and V2(x), construct an approximate triangular wave signal.

[0056] The above process transforms the nonlinear sine and cosine signals into approximate triangular wave signals, directly obtaining the displacement value without arctangent calculation. The interval-coded signal divides the obtained approximate triangular wave signal into 16 intervals. When the displacement measurement accuracy requirement is not high, the interval-coded signal can be directly used to achieve a 16-fold coarse-to-fine subdivision of the grating moiré fringes. For fine subdivision, the maximum subdivision factor equals the number of interval divisions multiplied by the number of segments each interval can be divided into (determined by linearity). This invention divides a one-cycle sine and cosine signal into 16 intervals, with a maximum linear error of 0.0039% per interval. Compared to the prior art "A Grating Moiré Fringe Subdivision Method," which divides a one-cycle sine and cosine signal into 4 intervals with a maximum linear error of 0.39% per interval, this invention achieves a higher subdivision factor.

[0057] Step 3: Construct a coefficient-compensated signal based on the sine and cosine digital signals; the expression for the coefficient-compensated signal is:

[0058] C(x) = 0.0102 × V3(x) 3 -0.0661×V3(x) 2 +0.0012×V3(x)+1.0547

[0059] Wherein, C(x) represents the coefficient compensation signal, and V3(x) represents the approximate triangular wave signal.

[0060] Step 4: Compensate the approximate triangular wave signal to obtain a triangular wave signal whose amplitude is linearly related to the grating displacement; the specific process is as follows: compensate the approximate triangular wave signal through the coefficient compensation signal, the expression is: V4(x)=V3(x)C(x);

[0061] Where V4(x) represents the triangular wave signal, V3(x) represents the approximate triangular wave signal, and C(x) represents the coefficient compensation signal.

[0062] The triangular signal wave obtained by supplementing with coefficient compensation signal can improve the linearity of the approximate triangular wave signal, thereby enabling higher magnification subdivision.

[0063] Step 5: Divide the triangular wave signal into multiple intervals using interval coding signals, and linearly combine the multiple intervals to obtain a sawtooth wave signal that is proportional to the grating displacement.

[0064] Since the four-bit interval encoded signal changes from 0000 to 1111 after one cycle of the sine and cosine signals, corresponding to decimal 0 to 15, the triangular wave signal with 16 intervals per cycle can be converted into a sawtooth wave signal based on the interval encoded signal. The resulting sawtooth wave signal has a linear relationship with the displacement, thus calculating the displacement information within one cycle.

[0065] Example 3

[0066] The sine and cosine signals output from the grating sensor are converted from analog to digital by an analog-to-digital converter to obtain a sinusoidal digital signal V. s (x) and cosine digital signal V c (x), such as Figure 2 As shown.

[0067] For the sinusoidal digital signal V respectively s (x) and cosine digital signal V c (x) Take the absolute value to obtain the absolute value of the sinusoidal digital signal |V s (x)|、Absolute value of cosine digital signal|V c (x)|, such as Figure 3 As shown.

[0068] The sinusoidal digital signal V will be respectively s (x) and cosine digital signal V c The comparison operation between (x) and 0 yields the sine interval encoded signal bit0 and the cosine interval encoded signal bit1, as follows: Figure 4 As shown.

[0069] The absolute value of a sinusoidal digital signal |Vs (x)|and the absolute value of the cosine digital signal|V c By comparing (x)|, we obtain the absolute value interval encoded signal bit2, such as Figure 5 As shown.

[0070] Based on the absolute value of the sinusoidal digital signal |V s (x)|and the absolute value of the cosine digital signal|V c (x)|Construct the tangent signal V1(x), such as Figure 6 As shown.

[0071] Construct the tangent signal V2(x) based on the tangent signal V1(x), as follows: Figure 7 As shown.

[0072] By comparing the two tangent signals, the tangent interval encoded signal bit3 is obtained, such as... Figure 8 As shown.

[0073] Based on the tangent signals V1(x) and V2(x), an approximate triangular wave signal V3(x) is constructed, as follows: Figure 9 As shown.

[0074] A schematic diagram illustrating the error e3(x) between the approximate triangular wave signal V3(x) and the standard linear signal is shown below. Figure 10 As shown.

[0075] A coefficient-compensated signal is constructed based on the sine and cosine digital signals.

[0076] The triangular wave signal V4(x) is obtained by compensating the approximate triangular wave signal with a coefficient compensation signal, such as... Figure 11 As shown.

[0077] The triangular wave signal is divided into 16 intervals using interval-coded signals. Linear combinations of multiple intervals yield a sawtooth wave signal proportional to the grating displacement. A schematic diagram illustrating the error e4(x) between the triangular wave signal V4(x) and the standard linear signal is shown below. Figure 12 As shown.

[0078] The four interval coded signals obtained in this embodiment are combined as follows: Figure 13 As shown. The interval division results and the expression for the sawtooth wave signal V5(x) are as follows. Figure 14 As shown in the figure. A schematic diagram of the resulting sawtooth wave signal V5(x), which is proportional to the grating displacement, is shown below. Figure 15 As shown, V5(x) is the displacement signal of the grating sensor within one cycle, which is proportional to the actual displacement. The actual displacement can be obtained without complex arctangent calculations.

[0079] The method of the present invention (i.e., the method of the present invention) is used in combination with the sine-cosine subtraction method, the tangent method, the sine phase shifting method, and a grating moiré fringe subdivision method to subdivide the grating moiré fringes. The division intervals, the maximum linear error of a single interval, and the theoretical maximum subdivision magnification are shown in Table 1.

[0080] Table 1

[0081]

[0082]

[0083] As shown in Table 1, compared with other methods, the maximum linear error of a single interval obtained by the method of this invention is significantly reduced, and the theoretical maximum subdivision ratio is significantly increased.

[0084] Through the above-described method, the linearization subdivision method for grating moiré fringe signals of this invention divides a one-cycle moiré fringe signal into approximately linear signals of 16 intervals by processing the original sine and cosine signals. Simultaneously, a compensation signal is proposed to improve the linearity of the constructed linear signals. This method uses only simple addition, subtraction, multiplication, division, absolute value, and comparison operations, enabling higher subdivision ratios.

Claims

1. A method for linearizing and subdividing a grating moiré fringe signal, wherein the grating moiré fringe signal is a sine or cosine signal, characterized in that, The specific steps are as follows: Step 1: Convert the sine and cosine signals output by the grating sensor from analog to digital to obtain sine and cosine digital signals; Step 2: Calculate the interval-coded signal based on the sine and cosine digital signals and the comparison operation, and construct an approximate triangular wave signal; Step 3: Construct coefficient compensation signals based on the sine and cosine digital signals; Step 4: Compensate the approximate triangular wave signal using the coefficient compensation signal to obtain the triangular wave signal; Step 5: Divide the triangular wave signal into multiple intervals using interval coding signals, and linearly combine the multiple intervals to obtain a sawtooth wave signal that is proportional to the grating displacement. The process of calculating the interval-coded signal in step 2 is as follows: For the sinusoidal digital signal V... s (x) and cosine digital signal V c (x) Take the absolute value to obtain the absolute value of the sinusoidal digital signal |V s (x)|、Absolute value of cosine digital signal|V c (x)|;The sinusoidal digital signal V is respectively... s (x), cosine digital signal V c The comparison operation between (x) and 0 yields the sinusoidal interval encoded signal. Sum and cosine interval encoded signal The absolute value of a sinusoidal digital signal |V s (x)|and the absolute value of the cosine digital signal|V c By comparing (x)|, the absolute value interval encoded signal is obtained. Based on the absolute value of the sinusoidal digital signal |V s (x)|and the absolute value of the cosine digital signal|V c (x)|Construct the tangent signal Construct the tangent signal based on the tangent signal V1(x) By comparing two tangent signals, the tangent interval encoded signal is obtained. The sine interval encoded signal bit0, the cosine interval encoded signal bit1, the absolute value interval encoded signal bit2, and the tangent interval encoded signal bit3 are the interval encoded signals; The specific process of constructing the approximate triangular wave signal is as follows: construct the approximate triangular wave signal based on the tangent signal V1(x) and the tangent signal V2(x). ; The expression for the coefficient compensation signal in step 3 is: C(x)=0.0102×V3(x) 3 -0.0661×V3(x) 2 +0.0012×V3(x)+1.0547 Where C(x) represents the coefficient compensation signal and V3(x) represents the approximate triangular wave signal.

2. The method for linearizing and subdividing grating moiré fringe signals according to claim 1, characterized in that, Step 4 is as follows: the approximate triangular wave signal is compensated by the coefficient compensation signal, and the expression is: V4(x)=V3(x)C(x); Where V4(x) represents the triangular wave signal, V3(x) represents the approximate triangular wave signal, and C(x) represents the coefficient compensation signal.

3. The method for linearizing and subdividing grating moiré fringe signals according to claim 1, characterized in that, The amplitude of the triangular wave signal in step 4 is linearly related to the grating displacement.

4. The method for linearizing and subdividing grating moiré fringe signals according to claim 1, characterized in that, The analog-to-digital conversion of the sine and cosine signals output by the grating sensor in step 1 is performed within the analog-to-digital converter.

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