Diagonal Field of View (FOV) at a Specific Image Distance: Values provided at different image distances (e.g., 124° @ 10mm)

The F*tan(theta) method is a more general approach to calculating distortion. It’s often used for initial distortion assessment in various lenses, including photographic lenses. This method helps understand how straight lines deviate from their ideal positions due to distortion.

Lens datasheets often include distortion information to help photographers and engineers understand how the lens behaves. Lens distortion refers to the phenomenon where straight lines in a scene appear curved in the final image. This happens because lenses don’t perfectly focus light from all parts of the field of view.

F-Tan (Theta) method uses the tan(theta) relationship to calculate a reference height based on magnification, and the F(Theta) method uses F*theta (radians) to represent the ideal image point location based on its angular position.

Imagine a scene with a square grid. In barrel distortion, the grid would bulge outwards, making the squares appear wider on the edges. Meanwhile, in pincushion distortion, the grid would sink inwards, making the squares appear narrower on the edges. Mustache distortion would cause the grid lines to become wavy.

Pincushiondistortion

This is because when we perceive an object as white, we are seeing all the colors on the visible light spectrum bouncing off the object and hitting our eye, ...

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The formula calculates the difference between the expected height of an object based on the sensor size and its actual distorted height based on the distortion values and field of view. This difference is then expressed as a percentage of the vertical sensor size to provide a measure of barrel distortion.

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Pincushiondistortionlens

The SAR and B1+rms calculator has been updated to version 2.2. This uses a more realistic model (assumes the body within the RF coil is a uniform cylinder, rather than a sphere). It also calculates the average (whole body) SAR whereas before it calculated the peak SAR- so it doesn’t so easily jump out of the Normal … More SAR and B1+rms calculator update

Tangentialdistortion

MR signal and contrast calculator (SE) The MR signal and contrast calculator or app lets you choose two tissue T1 and T2 whilst manipulating the scanner parameters: TR and TE to show the signal, contrast and relative contrast to noise ratio (CNR). Use the calculator to explore the weightings below. MR gradient echo signal and … More MR signal and contrast calculators

Feb 5, 2023 — The mathematical description of aspheric lenses is based on a surface profile equation that defines the shape of the lens surface. This equation ...

Distortionaberration

Use the SNR and resolution calculator to investigate the effect of various parameter changes in MRI. The calculator reports the relative (to default parameters) SNR, pixel size and scan time. Reloading the page will restore the default values. Note: this works best on a computer. It will also work on Android and IOS mobile devices. … More SNR and resolution calculator

TV Distortion, as the name suggests, originated in the context of television applications. It can be calculated using the following formula:

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Optical distortion represents the overall distortion parameter of the optical system. F-Tan theta or optical distortion can be calculated using the following formula.

In this blog, we break down distortion parameters in lens datasheets and the three ways in which distortion is represented.

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The F-Tan (Theta) method uses the tangent function to relate the angle to object size and magnification. Whereas the F(Theta) method focuses on the angular position of the image point relative to the centre. Both the methods require the focal length (F) and the diagonal FOV (degrees). But in the F(Theta) method the FOV in degrees is converted to radians.

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F*tan(theta) calculations are used in camera calibration processes, where distortion parameters are estimated for correcting captured images. Lens designers often utilize F*tan(theta) calculations during the design phase to predict and minimize distortion in the final lens. This helps create lenses with minimal image curvature and ensures accurate image reproduction.

RadialdistortionFormula

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A negative value indicates barrel distortion (objects appear smaller towards the edges). In the above example, the calculation shows a higher barrel distortion (-39.5%) at a larger image distance (10mm). As the image distance decreases (9mm and 5mm), the distortion percentages become less negative, indicating a decrease in the barrel effect.

F(Theta) method focuses on the angular relationship between the ideal undistorted image point and the actual distorted image point without needing magnification information.

First choose the tissues you are interested in. Alternatively T1 and T2 values can be entered as “free”.Then select your scanning TR and TE (for spin echo).The graph shows the signal intensity (max = 1) for both tissues, the contrast and the relative contrast to noise ratio (CNR). The relative grey scale for the two … More MR signal and contrast calculator (SE)

Brown-Conradydistortionmodel

Barreldistortion

Part of Photonics Media's celebration of the 50th anniversary of the laser, this chart lists the major types of commercial lasers available in wavelengths ...

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LensdistortionExamples

First choose tissue T1 and T2 values.Then select your scanning TR, TE  and flip angle. You can also set a field inhomogeneity factor. The calculator uses an estimated value of T2* based upon this and the tissue T2.The graph shows the signal intensity (max = 1) for both tissues, the contrast and the relative contrast … More Gradient echo signal and contrast calculator

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Mathematically, distortion can be represented in three different ways in the lens datasheet; let us look at each of them in detail.

F-Theta lenses are specifically designed to maintain a constant image size (or spot size for lasers) across a scan field. The F-Theta calculation helps ensure the accuracy of this constant size by measuring deviations from the ideal. These lenses are used in various applications like laser marking and engraving, laser cutting, 3D printing and LiDAR.

Both methods can be used to estimate distortion, but they can be more applicable in certain situations. F-Tan (Theta) is preferred when the focus is on object size and magnification changes due to distortion. And the F(Theta) method is used to get the angular relationship of distorted image points without needing magnification information.