Focal Length Calculator

Ensure a perfect fit for your resulting image within your sensor size using this calculation.
CALCULATE FOCAL LENGTH

Focal Length Calculator

Ensure a perfect fit for your resulting image within your sensor size using this calculation.
CALCULATE FOCAL LENGTH
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Focal Length Calculator

CALCULATE FOCAL LENGTH USING FOV AND SENSOR SPECS

INPUT

OBJECT SPACE
mm
mm

SENSOR SPECS


mm
Consult experts for support.
OUTPUT

SENSOR SPECS
mm
mm
mm


LENS SPECS
mm

OBJECT SPACE
deg
deg
deg

By utilizing this focal length calculator tool, you can determine the focal length needed to capture an image of an object at a specified distance. This calculation allows you to ensure that desired field of view will be captured by your optical module.

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What is Focal Length?

Focal length is a crucial parameter that directly affects the angle of view and magnification of the images you capture. Focal length is the distance between the optical origin and the image plane when parallel rays are focused to a single point in the image plane. It is typically measured in millimeters (mm) and determines how much of the scene will be captured and the perceived magnification of the object.

The focusing power of a lens and its focal length is inversely proportional. A lens with a longer focal length, when compared to a lens with a shorter focal length, will result in a smaller field of view and increased magnification of objects. The field of view can be expressed as a dimension in millimeters or degrees. When the sensor size (H), desired field of view (FOV), and working distance (WD) are known, it is possible to estimate the required focal length (f) of the lens using the following equation.

It is important to note that this approximation is valid primarily for objects that are significantly distant.

The angular field of view (AFOV), which represents the extent of the observable scene in degrees, can be derived from the field of view (FOV) and working distance (WD).

It should be noted that as the field of view widens, the resulting image may exhibit more distortion. In certain cases, distortion can be mitigated using dewarping techniques. However, it is advisable to select a lens optimized for the intended field of view to minimize distortion in the original image.

Inverse correlation between focal length and field of view (Constant Sensor Size)

How Does the Focal Length Calculator Work?

Focal length calculator takes into account the image size, object distance, and object size to recommend the most suitable lens focal length for your specific application. Here’s how it works:
  1. The user inputs the working distance (WD), horizontal field of view (FOV), vertical FOV, number of pixels (horizontal), number of pixels (vertical), and pixel size.
  2. The sensor size is then calculated horizontally, vertically, and diagonally. We are using the basic formulas for calculations of Horizontal, Vertical and diagonal Senzor Size. Note the difference between: – Active Pixel Area: The active pixel area refers to the physical area on an image sensor that is sensitive to light and captures the actual image data. – Effective Pixel Area: The effective area of a CMOS sensor includes the shielded optical black over-scan area, which generates an average dark current and voltage bias level as a reference to the active pixels. – Recommended Pixel Area: refers to the recording area recommended by the sensor manufacturer.
  3. The magnification is then calculated using the formula: M=Horizontal Sensor Size/Horizontal Field of View
  4. Finally, the desired focal length is calculated based on magnification.

Focal Length Calculation – Basic Understanding

When it comes to focal length calculation in imaging systems, here are some important things to consider:
  1. Lens Formula: The focal length calculation is based on the lens formula, which states that the reciprocal of the focal length is equal to the sum of the reciprocals of the object distance and the image distance .This formula is derived from the principles of lens imaging in geometric optics.
  2. Object and Image Distances: To calculate the focal length, you need to measure the object distance (u) and the corresponding image distance (v). The object distance is the distance between the lens and the object being imaged, while the image distance is the distance between the lens and the image formed on the image sensor or film.
  3. Units: Focal length is typically expressed in millimeters (mm) for photographic lenses. Make sure to use consistent units for object and image distances to obtain accurate results.
  4. Thin Lens and Paraxial Approximation: Focal length calculations assume the lens is thin and the light rays are close to the optical axis, leading to a simplified analysis known as the paraxial approximation. This approximation is valid for many practical situations but may not hold true for complex optical systems or specialized lenses.
  5. Sign Convention (Single element lens): Focal length can have positive or negative values, depending on the lens type. A positive focal length represents a converging lens (e.g., a convex lens), while a negative focal length represents a diverging lens (e.g., a concave lens).
  6. Multiple Lenses or Lens Systems: In cases where multiple lenses or lens systems are involved, the total focal length can be calculated by using more advanced lens combination formulas.
  7. Calibration and Precision: Focal length calculation requires accurate measurement of object and image distances. Calibration of measuring instruments and careful measurement techniques are essential to ensure precise results.
  8. Limitations and Considerations: Focal length calculation assumes idealized conditions and may not account for factors such as lens imperfections, aberrations, and distortion. These factors can affect the actual performance of lenses in real-world imaging systems.
By understanding these key aspects, you can perform focal length calculations to determine the characteristics of lenses and their impact on imaging systems, enabling you to choose appropriate lenses for specific applications.

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FAQ

In imaging systems, the focal length refers to the distance between the optical origin and the image sensor or film when a distant subject is in focus. It determines the magnification and field of view of the captured image.

The focal length of a lens for a single element lens system can be calculated using the lens formula:

Where:

  • f represents the focal length of the lens
  • u is the object distance (distance between the lens and the object)
  • v is the image distance (distance between the lens and the image formed)

By measuring the object distance (u) and the corresponding image distance (v), you can substitute these values into the lens formula and find the focal length (f). It’s important to know that the focal length of photographic lenses is usually expressed in millimeters (mm).

Keep in mind that this formula assumes thin lenses and a paraxial approximation, which are valid for many practical situations. However, for complex optical systems or special lenses, additional considerations and corrections may be required for accurate calculations.

In single lens element system, a positive focal length indicates a converging lens, also known as a convex lens, which brings light rays together to form a real image. A negative focal length represents a diverging lens, also called a concave lens, which spreads light rays and forms a virtual image.
The magnification produced by an imaging system is given by the formula: Where:
  • M represents the magnification
  • v is the image distance
  • u is the object distance
A longer focal length (larger f value) generally results in a larger magnification, while a shorter focal length (smaller f value) leads to a smaller magnification.
The field of view (FOV) is in general inversely proportional to the focal length of the lens. For a given sensor size, a shorter focal length (wide-angle lens) typically captures a wider field of view, while a longer focal length (telephoto lens) narrows the field of view.
The depth of field (DOF) is influenced by the focal length, aperture size, subject distance, sensor pixel size. Generally, shorter focal lengths (wide-angle lenses) result in a wider depth of field, while longer focal lengths (e.g. telephoto lenses) tend to produce a shallower depth of field.
Zoom lenses have a variable focal length, allowing you to adjust the magnification and field of view. Longer focal lengths in zoom lenses enable greater magnification and are useful for capturing distant subjects.
Zoom lenses have a variable focal length, allowing you to adjust the magnification and field of view. Longer focal lengths in zoom lenses enable greater magnification and are useful for capturing distant subjects.
In most imaging systems, the focal length of a lens is fixed and cannot be changed. However, variable focal length systems allow you to achieve different magnifications.
The bokeh effect refers to the aesthetic quality of the out-of-focus areas in an image. Focal length, along with other factors like aperture size and subject distance, influences the depth of field and, consequently, the appearance of the bokeh. Longer focal lengths (telephoto lenses) often produce a smoother and more pronounced bokeh effect.
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