Focal length of a pair of lenses - optics - focal length of lens formula

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• Full-frame fisheye lenses (diagonal or rectangular) have an image circle that extends beyond the sensor area, with a 180-degree angle of view from corner to corner. Horizontal and vertical angles are less than 180 degrees, varying by lens. For example, a 15mm equisolid angle lens has a 180-degree diagonal view, 147-degree horizontal view, and 94-degree vertical view.

A fisheye lens offers a large depth of field, allowing sharp focus in both the foreground and background of an image. The focal length of fisheye lenses is short and its value is determined by the sensor format. For a (35 mm film) full frame sensor, usually the focal length of fisheye lenses is not larger than 10 mm for circular images, and not larger than 16 mm for full-frame images. The focal length of fisheye lenses can be as short as 1 to 2 mm for digital cameras using smaller electronic imagers such as, 1⁄4 “, 1⁄3″ and 1⁄2” format CCD or CMOS sensors.

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Shanghai Optics can optimize the entire process of designing and producing these fantastic lenses, which can help you receive high quality fisheye lenses in efficient ways.

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A fisheye lens is a type of ultra wide angle lens which can capture an extremely wide field of view. While a rectilinear wide-angle lens can capture a field of view of 100 degrees, a fisheye lens can capture a field of view ranging from 100 to 180 degrees, producing a circular image. These lenses introduce a large amount of barrel distortion, and straight lines are only possible at the center of the frame. They are specifically designed to create a wide panoramic or hemispherical view without blind spots. Fisheye lenses are widely used in various applications, such as sky and dome movie projection in planetariums, surveillance cameras, car cameras, security cameras, and scientific photography.

The following figures show the design and imaging performance of a fisheye lens with a focal length of 14mm, f/number of 2.8. The lens is designed to work at the visible and near infrared wavelength range and have a 180-degree field of view over the diagonal of a 35mm film (full frame) format. The fisheye lens has a F-Tan(Ɵ) distortion of -100% at the edge of the image circle. The F-theta distortion of this lens is lower than 3%. The MTF is above 30% at spatial frequency of 631p/mm over the entire field of view. The relative illumination is above 50% at the edge of the viewing angle.

Fixed magnification compact beam expanders, designed for 1064 nm, 532 nm and 355 nm laser lines. Beam expansion ratios from 2X to 10X available.

• Circular fisheye lenses have a 180-degree angle of view, projecting a hemisphere onto a circle within the frame, resulting in black corners.

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The Compact Beam Expander is designed to increase the diameter of a collimated input beam to a larger collimated output beam. EKSMA OPTICS offers compact Galilean type beam expanders for 1064 nm, 532 nm and 355 nm wavelengths. The Compact Beam Expander has a possibility to be adjusted for the input beam divergence angle to obtain collimated, divergent or focused beam at the output.

• Cropped circle fisheye lenses (portrait fisheye) are optimized for the width of the format cameras, producing images cropped at the top and bottom.

We design and produce high quality fisheye lenses that are used in a wide range of digital cameras with sensors from 1⁄4 “, 1⁄3″ and 1⁄2” to large format including fourth thirds sensor and 35mm film format. At Shanghai Optics, we have over 55 years of design and manufacturing experience to provide high quality designs and custom lenses for our customers.

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To capture the entire hemisphere with a fisheye lens, strong barrel distortion must be introduced. The image close to the edge needs to be compressed compared to the center of the image. When using the traditional f-tanθ projection method to calculate the image height, fisheye lenses with a 180-degree FOV can exhibit -100% distortion at the edge of the image circle. The following figures show the f-tanθ distortion and the resulting image of a rectilinear object.

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Based on how the image circle fulfills the camera sensor, camera fisheye lenses can be categorized by two different types: diagonal fisheye lens and circular fisheye lens. A diagonal fisheye lens refers to a fisheye lens which is designed to have a 180-degree field of view over the sensor diagonal. For this kind of fisheye lens, the actual horizontal and vertical angles of view of the rectangular image are smaller than 180 degrees. A circular fisheye lens refers to a fisheye lens which is designed to have a 180-degree field of view over the sensor width. Since an image sensor usually is rectangular and diagonal length is larger than the fisheye image circle diameter, the corners of the image are completely black.

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Feb 17, 2020 — How close do you want to focus? The farther away, the less focusing travel you need given focal length. The lens' rear node (for most LF lenses, ...

As a unique type of camera lens, fisheye lenses have some special properties when compared to other ordinary camera lenses. A fisheye lens should be an inverted telephoto lens due to the large FOV and short focal length. In order to direct all the light rays from an entire hemisphere into the aperture stop, fisheye lenses usually have more than one negative lens element in the front group to reduce the ray angles. The rear group of the fisheye lens needs to be positive to compensate for the total power of the lens. For accurately tracing the rays of a fisheye lens with large pupil aberration, the ray aiming algorithm needs to be turned on in the optical design software.

by SL Renne · 2023 · Cited by 1 — You can see quite a few numbers, but you already know the magnification factor! To calculate the diameter (d) in mm you just need to divide the width of your ...

by VE Leshchenko · 2015 · Cited by 59 — For instance to achieve 95% efficiency (ηI) under D0 = 10 mm σθ should be less than 8.4 µrad. Whereas for combining of 20 mm beams with 95% efficiency σθ should ...