__Infrared Focal Plane __Array (IRFPA) imaging technology has the advantages of good concealment, smog penetration, low-light night vision, etc., and has been widely used in meteorological remote sensing, industrial inspection, medical imaging, military equipment and other fields. With the advancement of technology, the performance of IRFPA has been significantly improved, but the non-uniformity of spatial noise is still relatively poor [1], which seriously restricts the quality of infrared imaging and application performance.

The non-uniformity of the readout circuit (Read Out Integrated Circuit, ROIC) has become one of the main bottlenecks that limit the development of IRFPA [2]. Due to the complex sources of non-uniformity of IRFPA and the difficulty of improving the process, most researches focus on non-uniformity correction algorithms [3-4]. For the readout circuit, reference [5] analyzed the noise characteristics of the readout circuit using a three-dimensional noise model; reference [6-8] analyzed and simulated the non-uniformity of the readout circuit with different structures; reference [9] A readout circuit with on-chip correction function is proposed; reference [10] improves the off-chip correction method by using the structural characteristics of the readout circuit. However, the public literature lacks clear theoretical analysis and discussion on the overall design, analysis and simulation methods of ROIC heterogeneity.

Summarize the non-uniformity elements into input items and state items, and use the Taylor series expansion of dynamic nonlinear system equations to establish a general model of unit circuit non-uniform transmission to solve the problem of differences in unit circuit structures; by establishing equal-dimensional and equal-length transmission matrices Simplify the digital-to-analog circuit coupling process in the row-column serial-to-parallel conversion transmission process, and establish its non-uniform overall transmission model according to the general structure of the analog readout circuit; solve the problem of spatial local correlation of state parameters by introducing Perlin noise [11] ; Use the spatial component of the three-dimensional noise model to characterize the non-uniformity index, carry out numerical simulation and statistical analysis on the non-uniformity of the readout circuit, and provide effective theoretical guidance for the overall design and engineering optimization of the readout circuit.

1. Modeling of system heterogeneity

1.1 Cell heterogeneity model

The generalized non-uniformity refers to the unit output of the infrared imaging system, that is, the spatial inconsistency of the pixel gray value. Narrow non-uniformity generally refers to various non-uniformity evaluation indexes. Due to various complex reasons, various components of the infrared imaging system, such as infrared radiation scene, atmospheric transmission channel, infrared optical system, focal plane array, readout circuit, application electronic system, display system and working environment, etc., have non-uniformity. , and has the property of step-by-step transmission. Using the differential equations of the nonlinear dynamic system as a general abstract model of the heterogeneity of each subsystem can solve the differences in the composition properties of the respective systems. The equations are shown in formula (1):

In the formula: t is the time variable; u(t) is the input variable; x(t) is the state variable; y(t) is the output variable; x˙(t) is the first derivative of the state variable; f(⋅) and h(⋅) are time-domain functions. The state variable may contain multiple state parameters, namely:

Equation (1) shows that the non-uniformity of the system has time-varying characteristics, which will cause problems such as time failure of the calibration method. According to the generalized non-uniformity, without considering its time-varying characteristics and the specific change relationship of state variables, we can get:

In the formula: ij is the spatial position of the pixel; Δuij is the spatial fluctuation of the input variable; Δxij is the spatial fluctuation of the state variable; Δyij is the spatial fluctuation of the output variable. Engineering practice has proved that the infrared imaging system has local linear characteristics within the range of normal operating parameters. Therefore, the first-order Taylor series expansion of formula (3) can be obtained:

Formula (4) shows that output non-uniformity is related to the variable values of input variables and state variables and their partial derivative function values. When the value of the partial derivative function is always zero, it indicates that the system has no non-uniformity, otherwise the response of non-uniformity is a nonlinear function. Non-uniformity measurement is generally carried out at a certain working point, that is, y, x, u and their partial derivative function values are all definite values. Substituting it into formula (4) can normalize each variable into a relative variable, eliminate the huge difference in the physical dimension and value range of various variables, and facilitate the analysis of its cascade transfer characteristics. The simplified formula is as follows:

Equation (5) shows that the system output non-uniformity is determined by the input non-uniformity duij and state non-uniformity dxij and its relative gain composition. When the input variables have no non-uniformity or can be ignored, the state variable non-uniformity will still produce output non-uniformity. When the state variable has no non-uniformity or can be ignored, input non-uniformity will still produce output non-uniformity. Relative gain coefficient hx and hu is not always 1, indicating that the system nonlinearity will cause scaling of input non-uniformity and state non-uniformity.

1.2 ROIC heterogeneity model

At present, the mainstream IRFPA (infrared focal plane array) readout circuit is an analog row-column parallel-serial readout structure. The input unit array with the same size as the photosensitive element array integrates and amplifies the photocurrent, and simulates the pixel signal row by row under the control of the logic circuit. The output is conditioned and buffered, and finally the output buffer circuit performs multi-channel serial output [12]. The internal bias voltage, control logic and other circuits provide assistance for the analog link, as shown in Figure 1 as a whole.

**Figure 1.** Common architecture of analog ROIC

In order to reduce the output interconnection, the ROIC performs multiple parallel-to-serial conversions. Generally, the input unit array and the IRFPA array keep the same size, the multi-channel column buffer has a single row and the same column size, and the maximum size of the multi-channel output buffer is related to the array size. Small-scale is single-channel, medium-scale is 4-channel, and large-scale is 4-channel. 8 or more. This serial-to-parallel conversion will cause a significant change in the arrangement of the array data during transmission, which leads to difficulties in cascade analysis using formula (5). According to the structure in Fig. 1, the non-uniformity matrix of the column buffer circuit and the output buffer circuit can be modified with equal length, and the overall non-uniformity transfer matrix equation of the readout circuit can be obtained as shown in formula (7).

Where: h Indicates the partial derivative function value of each unit circuit; the subscript o, c, i represent the output buffer, column buffer and input buffer circuit respectively; the subscript y, x, u represent the output, state and output variable respectively; M, N, K Respectively, the row and column dimensions and the number of output channels of the IRFPA array; the matrix Du、Dxi、Dxc、Dxo Respectively represent the signal fluctuation transmission matrix of the photovoltaic pixel array, the input unit array, the column buffer circuit, and the output buffer circuit; the row vector Vxc

Is the state non-uniformity vector of the column buffer circuit; the row vector Vxo is the state non-uniformity vector of the output circuit; the function repmat(⋅) It is used to repeat the vector by the specified number of rows and columns to obtain a non-uniform transmission matrix of equal size.

2. Model simulation and analysis

The noise model, multi-channel transmission, nonlinearity, and a 320×256 readout circuit were modeled and simulated in Matlab, and qualitative and quantitative evaluations were performed using simulated images and spatial noise. Among them, the spatial noise can use four spatial noise items in the three-dimensional noise model [5]: frame spatial noise σs

is the root mean square of the entire frame of data, which is the same as the value of the non-uniformity index; row space noise σv

is the root mean square of the mean value of each row of data in the frame; the column space noise σh is the root mean square of the mean value of each column of data in the frame; pixel spatial noise σvh the margin after removing the row and column spatial noise for the frame spatial noise.

In the formula: dij is the data in row i and column j; D is the mean value of the whole frame of data; vi is the mean value of data in row i; hj is the mean value of data in column j.

2.1. Noise model non-uniformity

Spatial fluctuations of readout circuit parameters can be viewed as a type of random noise and simulated using a noise model with specific statistical characteristics. Since the fluctuation characteristics of the readout circuit parameters have a certain local spatial correlation, it is more suitable to use Perlin noise for simulation. However, due to the interpolation effect, the local value of Perlin noise is relatively smooth, which cannot reflect the influence of time-domain noise on spatial noise in the time-sharing sampling process. Influence. The Gaussian noise model basically has no local correlation, but it can simulate the time-space noise conversion characteristics of time-sharing sampling. Therefore, in this paper, Perlin noise is used to superimpose Gaussian noise to simulate the spatial fluctuation of the readout circuit. The simulation results are shown in Figure 2. In the figure, Perlin noise has obvious inter-row non-uniformity and inter-column non-uniformity, while Gaussian noise is mainly manifested as pixel non-uniformity.

**Figure 2.** Non-uniformity of noise model

2.2. Multi-channel non-uniformity

In the readout circuit, the pixel signal needs to be converted and transmitted through the multi-channel column buffer and output buffer circuit, and the state parameter difference between the channels will introduce significant non-uniformity. Assuming that the input signal and the input circuit are uniform and the system is completely linear, that is, the input non-uniformity is zero and the relative gain is 1, only the column buffer circuit and the output buffer circuit have state non-uniformity, the simulation results are shown in Figure 3 shown.

**Figure 3.** Non-uniformity of multi-chanel buffer

Figure 3 shows that the multi-channel column buffer and multi-channel output buffer circuit theoretically only introduce non-uniformity between columns, but the temporal noise (simulated with 1% Gaussian noise) in the time-sharing sampling process will be transformed into spatial noise, mainly manifested as A small amount of pixel non-uniformity, the magnitude is determined by the corresponding parameter temporal noise intensity and its noise suppression coefficient.

2.3. Nonlinear non-uniformity

In general, the nonlinearity of a readout circuit is defined as the ratio of the maximum deviation between the actual curve and the ideal curve to the maximum output swing within the voltage range of interest [2]. According to the definition of nonlinear error, combined with formula (5) and formula (7), the broken line model can be used for local linear simplification:

h=(H+dy/du)/H=1+dym/dum

In the formula: H is the coefficient of the system input linear response, let H=ymax/umax perform normalization to obtain the aforementioned nonlinear error dym, while dum and dym is the corresponding relative change in the input signal. The non-uniform gain curves of different nonlinear conditions can be obtained by using formula (10), as shown in Figure 4.

**Figure 4.** Non-uniformity of input responsibility non-linearity

When there is no nonlinearity (dym=0), the readout circuit does not scale the non-uniformity of the input signal (h=1), otherwise the nonlinearity will cause the non-uniformity of the input signal to scale, and the scaling ratio is the same as that of the nonlinear The amplitude and its rate of change are directly proportional. Generally, the nonlinear amplitude of the readout circuit can be controlled below 1% [13], but the conventionally defined nonlinearity cannot characterize the local nonlinear change, and when the local nonlinear change rate is large, it will also cause obvious nonlinearity. Uniform scaling. Therefore, the relative nonlinearity proposed in this paper, which considers the local rate of change, should be used when evaluating nonlinear inhomogeneity.

3. Simulation and optimization of a 320×256 circuit

3.1. Simulation and optimization process

The basic process of simulation optimization of a 320×256 circuit non-uniformity index guided by the model is shown in Figure 5.

**Figure 5.** Simulation process of non-uniformity optimization

3.2. Decomposition of non-uniformity index

The overall non-uniformity transfer model of the circuit is shown in formula (7), where M=256, N=320, K=4. Assume that the non-uniform data matrix Du in formula (7)、Dxi、Dxc、Dxo are independent random variables, combined with formula (9), it can be obtained: the decomposition formula of the non-uniformity index (frame space noise) of the circuit is as follows:

The non-uniformity index of the circuit output, namely σsy the design requirement is not more than 10%. On the whole, the non-uniformity is first divided into two parts related to the input and related to the circuit state. Temporarily assume that the two have the same influence, and substituting the formula (11) can be obtained:

According to the analysis in Section 2.3, temporarily assume that the initial boundary of the local relative nonlinear index of each coefficient in formula (12) is 10%, then substituting the above formula, the initial design requirements of the non-uniformity index of each subunit can be obtained as follows:

The input unit, column buffer, output buffer and other sub-circuits of the first layer of the circuit are all array structures, and the scale of their functional unit circuits is not large, so they can no longer be decomposed.

3.3. Unit circuit simulation and optimization

Currently, the readout circuit is mainly realized by CMOS technology, which has large intra-die device variations, that is, the parameters of the same device in different regions of the same chip are greatly different. Due to the large number of device parameters, foundries generally use a five-point process angle model that can cover the three-sigma deviation range to characterize the parameter deviation of the process line. In addition, temperature and voltage also have a significant impact on device parameters. Therefore, the combined conditions of PVT (Process, Voltage, Temperature) can be used to evaluate the spatial noise of the circuit.

Assuming that the spatial noise of the PVT parameters is independent of each other, the output spatial noise of the subunit circuit is the superposition of the four spatial noise responses. In order to eliminate the different state parameter gain hx

The unit and numerical difference of , the product of it and the state variable can be directly equivalent to the output variable dyij

. In addition, the state parameter space noise amplitude is very small, and the nonlinearity of the gain coefficient is not considered for the time being. Then the PVT non-uniformity model of the unit circuit is established according to formulas (5) and (7), as shown in formula (14).

Where: Dy represents the output spatial noise; DP、DV、DT represent the equivalent output noise of the PVT parameters, respectively. Based on this, the PVT simulation of the subunit circuit can be performed using the boundary conditions of the initial design and its non-uniformity can be obtained.

First, simulate the external design constraint T parameters. Use the initial condition of the T parameter of the circuit 80±0.1 K to scan the temperature deviation of the input and output response curves, and calculate the variance of the simulation data as the random variable DT

statistical variance. The simulation results of each sub-circuit show that the spatial noise caused by the 0.1 K temperature fluctuation is negligible.

Secondly, the V parameter has both external and internal constraints. In order to improve the adaptability of the circuit bias, the boundary of its initial condition is tentatively set at ±5%. There are many V parameters. For example, the column buffer unit circuit has 6 bias voltage inputs, which can scan the input and output voltage deviation one by one, and calculate the sum of the variances of all V parameter simulation data as the random variable DV statistical characteristics.

Third, use the five-point process angle model to scan the process deviation of the input and output responses, and calculate the variance of the simulation data as the random variable DP statistical variance.

Fourth, simulate the input and output nonlinearity of the current design, and calculate dym according to the simulation data and formula (10)

and its corresponding dum.

Finally, the non-uniformity of the subunit circuit is calculated according to formula (14) and formula (9), and then compared with the decomposed index to determine whether the design requirements are met, if not, the design needs to be optimized.

Table 1 shows the simulation results of the initial design of each subunit of the circuit. The non-uniformity of the three subunits does not meet the initial design allocation requirements, and an optimized design is required. Although the local relative nonlinearity is much higher than the conventional nonlinearity index, the highest input unit has only about 5.1% relative nonlinearity, which can meet the initial design requirement of 10%.

**Table 1.** PVT simulation of 320×256 ROIC

Circuit optimization mainly includes three parts: parameter optimization, structure optimization and overall optimization. If the current simulation results are close to the design requirements, first consider whether other sub-circuits are not sensitive to state noise, then compress their design indicators, and re-optimize the allocation of design indicators overall. Parameter optimization is mainly aimed at the P and V parameters. Scan the V parameter according to the sensitivity to determine its reasonable and acceptable lower limit, and then scan and optimize the parameters of the circuit components to find the area where the process angle has little influence on the circuit output. If the requirements still cannot be met, it is necessary to optimize the design of the circuit structure. The above optimization process requires multiple synthesis iterations.

After parameter optimization of the circuit, the state non-uniformity of the input unit and the output buffer unit decreased from 6.7% and 18.3% respectively to less than 1%, which can meet the initial distribution requirements. Although the state non-uniformity of the column buffer unit is 5.5%, it still does not meet the initial allocation requirements, but the simulation data is substituted into the formula (11) to calculate the overall non-uniformity index of the circuit output, which is about 7.8%, which can meet the overall index of 10%. Require. Therefore, reassigning the design indicators according to the current results, comprehensive consideration can temporarily end the design optimization process.

If the non-uniformity index of the subsequent improved circuit is required to be lower than 7.8%, the design needs to be further optimized, especially the structure of the column buffer unit circuit needs to be optimized.

3.4. Analysis of overall simulation results

The simulation results show that the readout circuit has obvious non-uniform characteristics, but it can be effectively reduced through design optimization. After a 320×256 circuit is optimized, the state non-uniformity of the input unit and output buffer unit drops from 6.7% and 18.3% to less than 1%, but the non-uniformity of the column buffer circuit is still 5.5%. Because the column buffer unit of this circuit uses more voltage-controlled current mirror modules in structure, parameter optimization alone cannot further reduce the non-uniformity, and structural optimization must be carried out.

According to the data in Table 1, it can be calculated that the non-uniformity of the readout circuit itself is 5.7%, of which the nonlinear non-uniformity is about 0.5%, and the state non-uniformity is about 5.6%. Therefore, the state non-uniformity plays a major role. The state non-uniformity mainly comes from the spatial fluctuation of the device process parameters and the spatial random fluctuation of the key bias parameters; since the temperature parameter of the readout circuit operates under low-temperature refrigeration conditions, the spatial fluctuation of the temperature parameter is small, and the influence on the non-uniformity is basically negligible. neglect. Although the relative nonlinear value of this circuit is higher than that of conventional nonlinearity, it still belongs to multiplicative noise, and the influence on non-uniformity is basically negligible.

Subjective image simulation and three-dimensional noise evaluation were performed on the simulation data before and after circuit optimization, as shown in Figure 6 and Figure 7, respectively. In the figure, the pixel array refers to the photovoltaic diode array; the input array refers to the input unit circuit array of ROIC; the column buffer refers to the multi-channel column buffer circuit of ROIC; the output buffer refers to the multi-channel output buffer circuit of ROIC; the output image refers to Final output of ROIC. Figure 6 shows that the non-uniformity of the readout circuit exceeds the non-uniformity of the input, resulting in a significant increase in output non-uniformity, and serious streak noise is superimposed on the output image, and the spatial noise of the output image is dominated by the spatial noise of the readout circuit. Figure 7 shows that after the circuit is optimized, the non-uniformity of the circuit is dominated by the spatial noise of the column buffer circuit. If the non-uniformity of the output image is to be further reduced, the optimized design of the column buffer circuit should be the main factor.

**Figure 6.** Non-uniformity before ROIC optimization

**Figure 7.** Non-uniformity after ROIC optimization

The non-uniformity simulation result based on this model is the standard deviation of the random sampling data of the output space noise of the readout circuit, which itself is also a random variable. The comparison with the test data of a single device is of little significance, and only the statistical values of a large number of device test data can be used for the derivation and correction of model parameters. In addition, since the spatial noise distribution characteristics of photovoltaic arrays and subunit circuits are different, the main sources of non-uniformity can be evaluated using statistical values of three-dimensional noise. For example, the column buffer circuit mainly exhibits low-frequency column spatial noise, the output buffer circuit mainly exhibits high-frequency column spatial noise, and the photovoltaic array and input unit mainly exhibit pixel spatial noise and row spatial noise.

Due to the limitation of testing methods, it is temporarily impossible to directly test and verify the readout circuit chip. Test verification mainly includes three aspects: chip test method, test data statistical model, and test data to model reverse transfer. Among them, the chip test method mainly considers the testability design of the readout circuit, including the design of the excitation injection circuit and the on-chip test circuit; the data statistical processing mainly considers the statistical model of small sample size and different data. The reverse transfer of model data is mainly based on the comprehensive consideration of non-uniform models and test methods to determine the parameters that can be transferred and the parameters that need to be tested.

Fig. 8 is a three-dimensional noise comparison diagram of the 320×256 circuit simulation results and the non-uniformity test data of 17 detector components. The black thick dotted line in the figure is the simulation result, the red line is the worst test data, and the blue line is the best test data. The comparison shows that most of the three-dimensional noise components of the test data are within the boundaries of the simulation results, and a small amount of data exceeds the boundaries of the simulation results. For the statistical characteristics of the sampling distribution, when the sample size increases, the mean value of the sampling test data will be close to the simulation results in this paper. Due to the fact that the test sample uses a screened readout circuit and the number is small, the sampling distribution tends to be in the form of a positive skewed distribution, making its mode better than the mean. In order to verify the accuracy of the model, the testability of the readout circuit must be optimized in the future, so that the readout circuit can be tested directly, and the test data can be accumulated and counted.

**Figure 8.** Simulation results vs test data of detectors

In addition to the above-mentioned test and verification issues, further research and testing on low-temperature models, statistical characteristics of noise and PVT parameters, and circuit optimization theory are required in the future.

4. Conclusion

According to the characteristics of the non-uniformity of the infrared focal plane imaging system, a method using the local linearization principle to establish the non-uniformity transmission model of the readout circuit is proposed, and it is proved theoretically that its non-uniformity is caused by nonlinear scaling and PVT parameter fluctuations It consists of two parts, of which the non-linear scaling part is generally negligible. According to the model, a 320×256 readout circuit was simulated and verified, and the statistical parameters of the non-uniformity model were obtained in combination with the circuit simulation, and qualitative and quantitative evaluation was carried out by using images and three-dimensional space noise. The results showed that: the non-uniformity of the readout circuit The inhomogeneity has a direct impact on the non-uniformity index of the detector.

This method can be used as an overall design evaluation tool for the non-uniformity of the readout circuit, and combined with circuit simulation to allocate and optimize the non-uniformity index, it supports the top-down non-uniformity design process of the readout circuit.

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