Numerical apertureof lens

To determine whether lens specifications are compatible, we need to find the resulting numerical aperture from the other three specifications. To do this we will first need to use the equation below to relate the image height h, focal length f and the half field of view Θ. This equation can be derived using simple geometry using the relationships shown in the red triangle in figure 3.2.

If the medium is not air, as is common for some microscope objectives, the approximation above can be multiplied by the index of refraction of the medium as shown below.

b) CMOS (Complementary Metal-Oxide-Semiconductor): CMOS sensors have gained popularity and are now the most common type of sensor used in digital cameras. As well, it is also used in other electronics gadgets such as phones and tablets and more. They offer several advantages, including lower power consumption, faster readout speeds, and better noise performance.

Numerical aperture formulaexample

Numerical aperture (NA) refers to the cone of light that is made from a focusing lens and describes the light gathering capability of the lens (similar to f/# ). NA is defined by the following equation, where n is the index of refraction of the medium (often n=1 for air), and α is the half angle of the cone of light exiting the lens pupil.

a) CCD (Charge-Coupled Device): CCD sensors use a complex process to convert light into digital signals. CCD sensors were popular in earlier digital cameras due to their high image quality. However, they consume more power and are slower than CMOS sensors, making them less common in modern devices.

Most camera sensors utilize a Bayer filter array to capture color information. The Bayer filter is a grid of red, green, and blue color filters placed over each pixel. Each pixel on the sensor captures only one color component (red, green, or blue). The missing color information for each pixel is interpolated based on the surrounding pixels during image processing.

In order to equate NA and f/#, we can use simple geometric relationships. Figure 3.1 shows a simple lens focusing light rays (blue lines) from infinity to a point. This creates a cone of light that can be described by numerical aperture using the previous equation. The half angle, α, can now be defined by the following equation:

Numerical apertureunit

Numerical apertureof optical fiber

Often times when starting the design process one can inadvertently request conflicting specifications. This example will show how easy this is to do and how to avoid it when specifying a lens.

Below are three sets of lens specifications that would result in the desired system NA. There is an infinite number of specifications that will give the desired NA if one is allowed to change more than one spec.

Numerical apertureof microscope

Now we can find the focal length of the lens by assuming that the customer wants entrance pupil diameter to stay at the specified 20mm.

Understanding how camera sensors work provides insights into the technical aspects of photography and helps you make informed decisions when selecting a smartphone or a digital camera. It also allows you to optimize settings and techniques to capture better images. Keep in mind that camera sensor technology is continuously evolving, with advancements in resolution, dynamic range, low-light performance, and other features. Stay updated with the latest developments to take full advantage of the capabilities of modern camera sensors.

Numerical apertureof objective lens

So what if the customer needs a numerical aperture of 0.25? To get this, at least one of the other specifications need to change. To do this, lets start with the initial specification for NA=0.25 and find what the f/# would be using this spec.

A camera sensor is an electronic device that converts light from the outside world into digital signals that are processed to create images. In digital cameras, it's essentially a grid of millions of tiny light-sensitive elements (pixels), where each pixel corresponds to a single point in the captured image.

Numerical aperture formulawith refractive index

Now that we have briefly explained what numerical aperture is, we can equate it to f/#. As explained here, f/# is also a measure of how much light can get through a lens. f/# of a simple lens is defined by the following equation, where f is the focal length of the lens and D is the diameter (or more specifically the entrance pupil diameter for more complex lens systems).

This is an exact equation relating the NA to the f/#, but it is often convenient to have an approximation for this. When n = 1 (medium is air) and if we use a small angle approximation (sin α ≈ tan α) then:

Numerical aperture formulain optical

After the sensor converts the light into digital signals, further processing is performed to enhance image quality. This includes noise reduction, white balance adjustment, color correction, and other image adjustments. The camera's image processor handles these tasks to produce a final image.

Digital camera sensors are the heart of every digital imaging device, from smartphones to professional DSLRs. Understanding how these sensors work can deepen your appreciation of photography and guide you in choosing the right device for your needs. This guide breaks down how camera sensors capture light, the types of sensors, key technologies, and factors influencing image quality.

Pixels are the individual light-sensing elements on a camera sensor. They capture the light that enters the camera lens and convert it into electrical signals. Each pixel consists of a photosensitive element and associated circuitry. The number of pixels on a sensor determines its resolution or the level of detail it can capture.

When light enters the camera through the lens, it passes through a series of optical elements (such as lenses and filters) before reaching the sensor. The light photons hit the surface of the pixels, generating an electrical charge proportional to the intensity of the light. This charge is then converted into a digital signal.

Once the image processing is complete, the camera's processor compresses the image and saves it in a file format such as JPEG or RAW. The image can then be stored on a memory card or transferred to a computer or other devices for further editing or sharing.