F-thetalensvs telecentric

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

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.

The correct identification and characterization of rocks is the foundation of any responsible mining and production of the minerals, metals and fuels that will shape our future. To provide this critical geological information, we developed the geoLOGr system (pronounced: geologger).

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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.

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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.

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.

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

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

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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.

Hyperspectral Intelligence develops cloud-based solutions that provide objective, real-time results for machine vision, hyperspectral imaging, and spectroscopy applications across industries.

F-ThetaLensPrice

The geoLOGr system consists of a compact and versatile hyperspectral rock scanner that collects hyperspectral data and high-resolution images from drill core and other geomaterials. The geoLOGr was designed to be robust, customer-operated, and cost-efficient.

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-ThetaLensfocal length

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.

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Over the last couple years, I have had many wonderful opportunities being contracted to work with Michelle, Ralf, and Derek from Hyperspectral Intelligence – a great company run by great people.

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Deliverables can be merged with geochemical, petrophysical, already existing hyperspectral, and other geological datasets to produce internally consistent outputs.

“Our experience with Hyperspectral Intelligence has been excellent. The data are of high quality and useful for us in practical applications, the geoLOGr is easy to use, and the HI team are wonderful to work with. They are responsive to all of our requests and needs. Their team has provided us with a very personalized service and it is a relationship which I appreciate and hope to grow in years to come. I have previously recommended their services to peers and colleagues and will continue to do so.”

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To date, the geoLOGr system has been successfully deployed at more than 50 projects around the world, ranging from the exploration to the production stage. The analytical results from the geoLOGr are used by geologists, metallurgists, and engineers to correctly identify and correlate rock units, distinguish ore and waste-rock, and to create better deposit models, thereby reducing the amount of time and money spent on a project.

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Hyperspectral Intelligence’s instrument, the geoLOGr, is one I have had the pleasure of operating, setting up, and instructing many personnel from around the globe about. It offers many solutions for a plethora of challenges that can occur acquiring and analyzing geological information. It is a user friendly yet adaptable/customizable machine that has had no problem meeting whatever needs a client may have. It is durable, dependable, and obtains quality data – say no more.

The geoLOGr is accompanied by world-leading, cloud-based data processing that is customized for each deposit. Compositional logs are produced rapidly and with unprecedented accuracy and sensitivity.

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We also provide various customization services, including camera enclosures, resolution, frame rate, and sensors of your choice, to ensure our cameras fit perfectly into your embedded vision applications.

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.

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Prabu is the Chief Technology Officer and Head of Camera Products at e-con Systems, and comes with a rich experience of more than 15 years in the embedded vision space. He brings to the table a deep knowledge in USB cameras, embedded vision cameras, vision algorithms and FPGAs. He has built 50+ camera solutions spanning various domains such as medical, industrial, agriculture, retail, biometrics, and more. He also comes with expertise in device driver development and BSP development. Currently, Prabu’s focus is to build smart camera solutions that power new age AI based applications.

The hyperspectral data from the geoLOGr are processed using a cloud-connected data processing infrastructure. Our highly-customized and deposit-specific data processing enables us to produce results of unprecedented sensitivity and accuracy that can be easily integrated in existing workflows.

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

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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.

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

Hyperspectral Intelligence is a geologist-lead company that develops innovative hyperspectral rock analysis equipment and advanced data processing technologies for the energy & modern mining industry.

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.