11. Camera and lens

brief introduction

For a camera , One of the most important components is the lens , It is the key to imaging , Whether small hole imaging or lens imaging

Secondly, we know that the shutter of the camera is always closed , It won't open until the moment you press the button to take pictures , Allow light information to enter the lens

Last , When the shutter is opened, the light successfully passes through the lens , All the light information will shine on the sensor ( Equivalent to film ) To store , Get the final image through the information on the sensor

Corresponding to the sensor here , What should it store

The right side is equivalent to the sensor plane , Each point of the sensor records light from all directions of the object , So every bit of storage is irradiance

Keyhole imaging and field of view (FOV)

This technology has a long history , Only light in a certain direction is allowed to pass through the small hole , To get an inverted image

There is not much explanation for small hole imaging , The main purpose is to introduce the concept of field of view through it

The angle range that can finally be imaged is called the field of view (Field of View), In the figure h hh Refers to the length of the sensor ,f ff Refers to the focal length of the lens ( Although keyhole imaging has no focal length , This can be used as the vertical distance from the sensor to the hole ), Through these two parameters , It's easy to calculate FOV

In general , We stipulate that the length of the negative sensor is 35mm when , be


As you can see from the diagram , When the focal length is larger , The smaller the imaging angle, the smaller the focus on a small part , It's similar to the magnification of our mobile phone

Of course, except for the focal length , The length of the sensor also has a significant impact , The longer the negative is , natural FOV And the bigger

For different devices , Sensors vary in length , Want to keep the same FOV Words , You need to reduce the focal length year-on-year

Exposure (Exposure)

What the sensor receives is irradiance, That is, the light power received per unit area , And exposure is multiplied by time irradiance

From the physical point of view, it is the real received energy (Energy)

time Controlled by shutter speed , besides , Exposure will be exposed by others in total 2 Values to control , That is, a total of 3 individual

• shutter speed (Shutter speed), The longer the shutter opens , The longer the light entering time , Naturally, the more light enters .
• Aperture size (Aperture size), The value describing this item is called f-stop, Intuitively understand that if the aperture is larger , That is, the less light blocked, the higher the degree of exposure .
• Sensitivity (ISO gain), The sensitivity can be simply understood as multiplying the final image value by a multiple .

First observe the bottom ISO The impact of changes on photos , Mentioned before ISO It's a simple linear change , Multiply the result of the image by a multiple , With ISO After a significant increase in the value of , Although the overall brightness of the picture will increase , But at the same time, you will also observe that the picture has a lot of noise . This is actually easy to explain , What photos record is nothing more than signals , So the information about light is naturally small noise Get into , If the overall brightness of the image is amplified ,noise Naturally, it will become more obvious and form noise

Then there is the shutter speed of the middle line , The higher the value at the bottom of the picture, the slower the speed , The longer the shutter opens , The greater the amount of light entering the lens , The brighter the picture will be , But at the same time, moving objects will also become blurred

After the shutter is opened, the camera records the light information of all objects for a period of time , If the shutter opens long enough , You can capture the movement of the object through the final photo , And this is dynamic blur

But this ambiguity is not necessarily a bad thing , As the example above shows , The shutter speed on the left is slow, which shows that the hammer tends to fall , Get more picture information , And the shutter speed on the right is fast , It looks more like a still picture , There is no dynamic effect

This is why the general film shooting only 24FPS But I won't feel Caton , Because the existence of dynamic blur makes the human eye receive more information . But for games, it often needs 60FPS above , Because every frame in the game is still, there is no dynamic blur ( Some games can turn on dynamic blur ), Therefore, it needs more pictures to make people feel not stuck

But there is one thing about shutter speed that needs extra attention , No matter how fast the shutter opens , It must have a process of opening and closing , Therefore, there is a small gap between the time intervals recorded in different parts of the whole picture , When shooting high-speed objects , This effect is more obvious

Finally, for the top line of the picture at the beginning , That is, the aperture size F-stop perhaps F-Number value ( The comma in the figure means decimal point ), The value can be simply understood as proportional to the reciprocal of the aperture diameter , therefore FN The smaller the value. , Represents the larger aperture , The greater the amount of light entering , The higher the brightness of the picture , But at the same time, it will also bring the influence of blurred depth of field

The above is about exposing some basic content , There are two main applications for exposure ： High speed photography and low speed photography ：

For high-speed photography , Objects move very fast , So you need a very small shutter speed to not find it , But at the same time, in order to compensate for insufficient light input time , You also need to use a large aperture or improve ISO To ensure normal exposure

For low-speed photography, the opposite is true , Generally, a longer shutter time is used to capture the trajectory of the object , As shown in the following figure, the landing trajectory of the aircraft

The depth of field (Depth of Field)

Properties of ideal lens

• All the light entering the lens in parallel will be concentrated at one point , Call this point the focus
• All light entering the lens from the focus will be emitted in parallel ( Optical path reversibility )
• The focal length can be changed at will ( Of course not with a single lens , But in reality, most cameras are a lens group , The focal length can be changed at will )

Using these properties, we can get the imaging law of the ideal lens , For an imaging object passing through a lens , Its object distance z o , Image distance z i And focal length f There is a relationship as shown in the figure below

The derivation process can simply start with two pairs of similar triangles


The causes of blurred depth of field

When a sensor plane is not above the truly accurate imaging plane of an object ( That is, the image distance mentioned before z i The plane of the ), There will be blur . As shown in the figure above , When the sensor plane is in the imaging plane calculated according to the lens imaging law Image Later on , A point passes through the lens to the sensor and becomes a line ( In three dimensions, it is a circle ), So there is ambiguity , Put the length after blur in the above figure C be called Circle of Confusion, Similarly, the triangle similarity is used to deduce as follows

It's not hard to see. ,C And prism length A In direct proportion to , The length of the prism is also proportional to the diameter of the aperture , So when the aperture is larger ,C And the bigger , At this time, the blurred depth of field is more obvious

( Left large aperture , Small aperture on the right ) It is obvious that the picture on the right should be clearer

Recall that I mentioned before , Aperture size F-Number The value is proportional to the reciprocal of the aperture diameter , More specifically ,N = f / D, That is, the focal length is larger than the diameter , So Convert Circle of Confusion The aperture diameter in the middle A = f / N （ here A And D equal ）, Get the formula shown in the figure below

At the same time, here are also examples of taking photos with different aperture sizes , Small aperture sharp , The depth of field is not obvious , The large aperture has obvious blurred depth of field

Depth of Field, It's not the same thing as blurred depth of field , Blurred depth of field is a situation , The depth of field is a specific value , It specifically refers to

When we fix an acceptable Circle of Confusion C The value of , It can be deduced in reverse that it is less than C What is the corresponding distance of the value , This distance is the depth of field , As shown in the figure below

Blue shaded areas C The value is less than the predetermined value , The length of this area is the depth of field

Realize depth of field blur in ray tracing

Simply simulate the light propagation of the lens

Actual rendering effect