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https://github.com/quanglv1996/machine-vision-infomation

The source code contains information and techniques about machine vision such as DoF, VoF, ...
https://github.com/quanglv1996/machine-vision-infomation

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The source code contains information and techniques about machine vision such as DoF, VoF, ...

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# Machine-Vision-Infomation

The source code contains information and techniques about machine vision such as DoF, VoF, ...



## [Pixel Size Physical](https://www.princetoninstruments.com/learn/camera-fundamentals/pixel-size-and-camera-resolution)

![Pixel Size](assets/pixel_size.png)



A pixel is the part of a sensor which ***collects photons*** so they can be converted into photoelectrons. Multiple pixels cover the surface of the sensor so that both the number of photons detected, and the location of these photons can be determined.



Pixels come in many different sizes, each having their advantages and disadvantages. Larger pixels are able to collect more photons, due to their increase in surface area. This allows more photons to be converted into photoelectrons, increasing the sensitivity of the sensor. However, this is at the cost of resolution.



Smaller pixels are able to provide higher spatial resolution but capture less photons per pixel. To try and overcome this, sensors can be back-illuminated to maximize the amount of light being captured and converted by each pixel.  



The size of the pixel also determines the overall size of the sensor. For example, a sensor which has 1024 x 1024 pixels, each with a 169 μm2 surface area, results in a sensor size of 13.3 x 13.3 mm. Yet, a sensor with the same number of pixels, now with a 42.25 μm2 surface area, results in a sensor size of 6.7 x 6.7 mm.



## [Camera Resolution](https://www.princetoninstruments.com/learn/camera-fundamentals/pixel-size-and-camera-resolution)

Camera resolution is the ability of the imaging device to ***resolve two point that are close together***. The higher the resolution, the smaller the detail that can be resolved from an object. It is influenced by pixel size, magnification, camera optics and the Nyquist limit. Camera resolution can be determined by the equation:

$$ 

Camera r Resolution = \frac{Pixel Size}{Magnification} * 2.3

$$

Where 2.3 compensates for the ***Nyquist limit***. This limit is determined by the Rayleigh Criterion of the sample.



## [Lens Resolution](https://www.princetoninstruments.com/learn/camera-fundamentals/pixel-size-and-camera-resolution)

It is also important to consider the resolution of the camera lens when determining the overall system resolution. The ability for a lens to resolve an object is limited by diffraction. When the light emitted from an object travels through a lens aperture it diffracts, forming a diffraction pattern in the image (as shown in Figure 3A). This is known as an Airy pattern, and has a central spot surrounded by bright rings with darker regions in-between (Figure 3B). The central bright spot is called an Airy disk, of which the angular radius is given by:



$$

θ = 1.22 * \frac{λ}{D}

$$



Where θ is the angular resolution (radians), λ is the wavelength of light (m), and D is the diameter of the lens (m).



## [Field of View (FoV)](https://www.princetoninstruments.com/learn/camera-fundamentals/field-of-view-and-angular-field-of-view)

![Field of View](assets/FOV.png)

***Field of view (FOV)*** is the maximum area of a sample that a camera can image. It is related to two things, the focal length of the lens and the sensor size.



* ***The sensor size*** is determined by both the number of pixels on the sensor, and the size of the pixels. Different sized pixels are used for different applications, with larger pixels used for higher sensitivity, and smaller pixels used for higher spatial resolution.

* ***The focal length of the lens*** describes the distance between the lens and the focused image on the sensor. As light passes through the lens it will either converge (positive focal length) or diverge (negative focal length), however within cameras the focal length is predominately positive. Shorter focal lengths converge the light more strongly (i.e. at a sharper angle) to focus the subject being imaged. Longer focal lengths, in comparison, converge the light less strongly (i.e. at a shallower angle) in order to focus the image.



![Angel Field of View](assets/FOV_C.png)



Schematic depicting how focal length has an impact on the angular field of view (AFOV). The shorter the focal length, the larger the AFOV, and vice versa for longer focal length. This influences the size of the FOV. Red line indicates light from the bottom of the object, creating the top of the image; blue light is light that is taken from the horizontal; grey lines indicate light that is from the top of the object, creating the bottom of the image. The height of the image is indicated by h.



## Calculating AFOV



![Calculate Angle Field of View](assets/AFOV.png)



$$

AFOV(°) = \frac{2}{tan(\frac{h}{2F})}

$$



where ***h*** is the horizontal dimension of the sensor and ***F*** is the focal length of the camera lens.



## Depth of Field (DOF)

![Depth of Field](assets/DOF.jpg)

**Depth of Field (DOF)** refers to the range of distance within a photo that appears acceptably sharp. It depends on several key factors:

- Focal length of the lens.

- Aperture (f-number).

- Distance to the subject.

- Circle of Confusion (CoC).



### Formula to Calculate DOF



The formula to calculate **DOF** is:



$$

DOF = \frac{2 \cdot N \cdot c \cdot H \cdot d}{(H - d)^2}

$$



Where:

- **N** = Aperture (f-stop)

- **c** = Circle of Confusion (CoC)

- **H** = Hyperfocal distance

- **d** = Distance from the camera to the subject



#### Hyperfocal Distance



The **hyperfocal distance** is the closest distance at which a lens can be focused while keeping objects at infinity acceptably sharp. It's calculated as:



$$

H = \frac{f^2}{N \cdot c}

$$



Where:

- **f** = Focal length of the lens (in mm)

- **N** = Aperture (f-stop)

- **c** = Circle of Confusion (CoC)



#### Example of DOF Calculation



To calculate DOF, we need to know:

- **Focal length (f)**: The focal length of the lens.

- **Aperture (N)**: The aperture setting (f-stop).

- **Circle of Confusion (CoC)**: Typically based on the camera's sensor size (e.g., 0.030 mm for a full-frame camera).

- **Subject distance (d)**: The distance from the camera to the subject.



##### Example:



Given the following values:

- Focal length (**f**) = 50 mm

- Aperture (**N**) = f/8

- Circle of Confusion (**c**) = 0.030 mm

- Subject distance (**d**) = 2000 mm (2 meters)



## Reference

[LENS CALCULATOR FOR STANDARD LENSES](https://www.get-cameras.com/Lenscalculator)



[LENS CALCULATOR FOR STANDARD LENSES](https://www.omnicalculator.com/other/camera-field-of-view)