A method of characterizing the linearity of a grating imaging system

Abstract

The present application relates to a method for characterizing the linearity of a grating imaging system. In the method, the intensity sinusoidal components of the first and second harmonic components of a sinusoidal amplitude grating can be described by an apparent transfer function, which can be modulated by changing the ratio of the intensity modulation of a specific frequency in the output to the intensity modulation of the corresponding frequency in the input. The method for characterizing the linearity of the imaging system using the apparent function has a clear structure and an intuitive expression, and the change relationship between the linearity of the imaging system and the coherence of the imaging system can be clearly seen.

Description

Technical Field

[0001] This invention relates to the field of optical imaging technology, and more specifically to a method for characterizing the linear relationship of a grating imaging system. Background Technology

[0002] Optical imaging technology, which can clearly present abstract phenomena to people in the form of images, has been widely used in fields such as medicine, education, military, and people's livelihood, which has also promoted the continuous development of optical imaging technology.

[0003] Imaging systems provide observers with more detailed and accurate visual information than what the naked eye can directly see. To fully understand the quantitative relationship between an object and its image, it is insufficient to merely know the properties of transmitted or reflected light and the laws governing light waves as they pass through optical instruments. It is also necessary to know the coherence of the light field away from the object, as coherence profoundly affects the final observed image. Furthermore, in real life, the light we receive is not always either truly incoherent or truly coherent—the two extremes—but more commonly, it is "partially coherent," falling somewhere in between. Therefore, research on imaging systems illuminated by partially coherent light is also essential.

[0004] Partially coherent light imaging systems are generally nonlinear systems, lacking a general transfer function. Therefore, the object-image relationship and information transmission capability need to be addressed. Patent application number "202110436259.0," entitled "Optical System Linearity Measurement Device and Method," proposes an optical system linearity measurement device. This device first adjusts the proportion of the light beam blocked by a light-blocking plate, allowing the beams to reach the optical system at predetermined proportions. Then, by acquiring readings of the optical system under different reception states, the linearity level of the optical system is calculated. While this method uses a simple light-blocking plate structure with minimal interference to the light beam, its research object is theoretically still a coherent light imaging system. It does not address the impact of partially coherent light on the system's linearity level. In reality, the light we receive is often not either incoherent or coherent, but rather partially coherent; even sunlight is not completely incoherent. Therefore, studying imaging systems illuminated by partially coherent light is of great significance. Partially coherent light imaging systems are typically nonlinear systems without a general transfer function, requiring a new evaluation method for the object-image relationship and information transmission capability of such systems. Summary of the Invention

[0005] This invention provides a method for characterizing the linear relationship of a grating imaging system, in order to solve the problem that existing technologies cannot quantify the relationship between the coherence of a partially coherent illumination sinusoidal amplitude grating imaging system and the changes in system coherence, thus making it difficult to give a quantitative relationship between the transmission capability between an object and its image.

[0006] To achieve the objectives of this invention, the technical solution adopted is: a method for characterizing the linear relationship of a grating imaging system, comprising the following steps:

[0007] Step 1: Define the ratio of the intensity modulation of a specific frequency in the output of the sinusoidal amplitude grating imaging system to the intensity modulation of the corresponding frequency in the input as:

[0008]

[0009] Step 2: The sinusoidal amplitude grating at a frequency of Input modulation In frequency Input modulation The modulation scheme at the output end is:

[0010]

[0011]

[0012] Where: “modulation” M represents the ratio of the peak amplitude of the sinusoidal fringe to the constant background; A i B i and C i In a partially coherent imaging system, the DC component and frequency of the output signal are respectively... The sinusoidal component and frequency are The coefficients of the three components of the sinusoidal component; The inherent spatial frequency of the sinusoidal amplitude grating object itself;

[0013] Step 3: The frequencies of the sinusoidal amplitude grating are respectively and When the intensity sinusoidal component is , its apparent function is:

[0014]

[0015]

[0016] Step 4: Based on the above calculation formula, plot the apparent transfer function curves of the first and second harmonic components under different coherence conditions.

[0017] σ=NA o / NA i NA o For the numerical aperture of an illumination optical system, NA i The numerical aperture of the imaging system.

[0018] Compared with the prior art, the advantages of the present invention are:

[0019] 1. The method of the present invention can quantitatively characterize the transmission capability of the first and second harmonic components of a sinusoidal amplitude grating when partially coherent light illuminates it.

[0020] 2. This invention characterizes the linearity of a polarization system imaging with sinusoidal amplitude gratings under different coherence conditions by changing the coherence degree. It can intuitively demonstrate the different linear relationships of the sinusoidal amplitude grating imaging system under different coherence degrees, providing quantitative guidance for fully understanding the quantitative relationship between an object and its image, and the transmission capability between them, thus enabling the acquisition of more refined and accurate visual information about the object.

[0021] 3. Among the methods for characterizing the linear relationship of imaging systems, no method using the apparent transfer function to characterize the linear relationship of a sinusoidal amplitude grating imaging system has been found. This invention, when using the apparent transfer function to characterize its linear relationship, introduces the concept of coherence, which allows for a direct view of the linearity level of the imaging system under different coherence conditions, making it applicable to a wider range of applications. Attached image description:

[0022] Figure 1 This is a schematic diagram of a partially coherent vector imaging system;

[0023] Figure 2 This is a schematic diagram of the apparent transfer function of the first harmonic component under different coherence conditions;

[0024] Figure 3 This is a schematic diagram of the apparent transfer function of the second harmonic component under different coherence conditions. Detailed Implementation

[0025] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0026] This invention provides a method for characterizing the linear relationship of a grating imaging system, wherein the imaging system is a polarization system of a sinusoidal amplitude grating illuminated by partially coherent light. See [link to relevant documentation]. Figure 1 This includes the light source, object plane, imaging lens, and image plane. Light emitted from the light source illuminates the object, passes through the imaging lens, and is received by the image plane, ultimately obtaining the light field information of the image plane. Here, β0 is the radius of the light source, α0 is the radius of the imaging lens, z0 is the distance between the light source and the sinusoidal amplitude grating, and z... i This is the distance between the imaging lens and the image plane.

[0027] Imaging systems based on partially coherent light illuminating a transmitted object are often nonlinear systems and, unlike linear systems, do not possess a general transfer function. For transmissive sinusoidal amplitude grating imaging systems, a special transfer function known as the transfer cross coefficient is obtained. The transfer cross coefficient's transfer capability also needs to be studied, leading to the concept of the apparent transfer function. The apparent transfer function is used to evaluate the transfer capability of the first and second harmonic components of the grating object in such nonlinear imaging systems. This invention modulates the apparent transfer function by changing the ratio of the intensity modulation of a specific frequency in the output to the intensity modulation of the corresponding frequency in the input. In other words, by changing the system's coherence, the apparent transfer function graphs of the first and second harmonic components of the sinusoidal amplitude grating under different coherence conditions are obtained. Finally, the apparent transfer function is used to characterize the linearity of the imaging system.

[0028] See Figure 2 and Figure 3 The vertical axis represents the value of the apparent transfer function, and the horizontal axis represents the value of the apparent transfer function. This represents the normalized grating spatial frequency, and the normalization process can be described as follows: from Figure 2 It can be seen that when parameter σ = 0, i.e., the hexagonal indicator curve, the effective light source is very small. At this point, the system can be considered a fully coherent imaging system with a frequency of... The apparent transfer function curve of the first harmonic component is similar to a step shape. The instantaneous value drops from 1 to 0; when parameter σ = 10, the triangular indicator curve indicates a very large effective light source. This system can be considered a completely incoherent imaging system, and the curve clearly shows a linear change. Therefore, the first harmonic component of the imaging system under this condition exhibits a linear change, while other parameters σ indicate a partially coherent system, with smaller σ values ​​indicating greater coherence. When parameter σ = 1, the dashed curve clearly deviates from a linear relationship; when parameter σ = 0.5, the circular indicator curve shows piecewise changes within the interval... The value inside is 1, within the interval The internal nonlinearity decreases to 0. Based on the above analysis, it can be seen that as the system coherence increases, the first harmonic component of this optical system gradually deviates from a linear system.

[0029] Figure 3 It can be seen that for the second harmonic component, under the condition of complete coherence with parameter σ = 0, the second harmonic component of the imaging system is nonlinear and exhibits a step-like variation. Similarly, in The instantaneous value drops abruptly from 1 to 0; in the completely incoherent case with parameter σ = 10, the second harmonic component of the imaging system exhibits a linear change; in the partially coherent system with other parameters σ, the change is clearly nonlinear, and a deviation from linearity is observed from σ = 1. At σ = 0.5, a piecewise change is also observed, within the interval... The value inside is 1, within the interval The internal nonlinearity is reduced to 0.

[0030] A comprehensive comparison of the apparent transfer function curves for the first and second harmonic components reveals that when σ = 10, i.e., under completely incoherent conditions, the system is linear, exhibiting a linear relationship for both the first and second harmonic components. As the coherence of the light source in the optical field imaging system increases, this system deviates further from a linear relationship.

[0031] The present invention provides a method for characterizing the linear relationship of a grating imaging system, comprising the following specific steps:

[0032] Step 1: The apparent function mentioned in this invention is the ratio of the intensity modulation of a specific frequency in the output to the intensity modulation of the corresponding frequency in the input, defined as:

[0033]

[0034] Step 2: The sinusoidal amplitude grating at a frequency of Input modulation In frequency Input modulation The modulation scheme at the output end is:

[0035]

[0036]

[0037] Where M is the "modulation degree", representing the ratio of the peak amplitude of the sine fringes to the constant background.

[0038] A i B i and C i In a partially coherent polarization imaging system, the DC component and frequency of the output signal are... The sinusoidal component and frequency are The coefficients of the three components of the sinusoidal component.

[0039] The frequency is the inherent spatial frequency of the sinusoidal amplitude grating itself.

[0040] Step 3: The frequencies of the sinusoidal amplitude grating are respectively and When the intensity sinusoidal component is , its apparent function is:

[0041]

[0042]

[0043] Step 4: Based on the above calculation formula, plot the apparent transfer function curves of the first and second harmonic components under different coherence degrees σ.

[0044] σ=NA o / NA i NA o For the numerical aperture of an illumination optical system, NA i The numerical aperture of the imaging system.

[0045] σ is used to evaluate whether the system is close to fully coherent or fully incoherent. When σ = 0, the system can be considered a fully coherent optical imaging system; when σ is much greater than 0, the system can be considered a fully incoherent optical imaging system. Whether the coherence characteristics of a partially coherent imaging system are closer to fully coherent or fully incoherent depends on the value of parameter σ. The apparent transfer function curves of the first and second harmonic components under different coherence conditions obtained in step four provide quantitative guidance on the transfer capability between the object and its image, thus enabling the acquisition of more refined and accurate visual information about the object.

[0046] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method of characterizing the linearity of a grating imaging system, comprising: The grating imaging system is a polarization system of a partially coherent light-illuminated sinusoidal amplitude grating, comprising the following steps: Step 1: Define the ratio of the intensity modulation of a specific frequency in the output of the imaging system to the intensity modulation of the corresponding frequency in the input as: Step two: the imaging system has a modulation at the input end at a frequency of a modulation at the input end at a frequency of a modulation at the output end of​​ Among them: "adjustment system" This represents the ratio of the peak amplitude of the sinusoidal fringes to the constant background amplitude. , and These represent the DC component and frequency of the output signal in a partially coherent imaging system, respectively. The sinusoidal component and frequency are The coefficients of the three components of the sinusoidal component; The inherent spatial frequency of the sinusoidal amplitude grating object itself; Step 3: The frequencies of the sinusoidal amplitude grating are respectively and When the intensity sinusoidal component is , its apparent transfer function is: Step 4: Calculate the coherence at different degrees based on the formula used in Step 3. Apparent transfer function curves of the first and second harmonic components ,in Numerical aperture for illumination optical systems, The numerical aperture of the imaging system.

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