Z stands for the surface (SAG) of the lens R is the Radius of curvature K: Conic constant Ax: Aspheric coefficient of xth order (can be null)

Optical lenses

There are different methods to measure the surface accuracy of an asphere which can be divided by contact measurements with probes and non contact measurements using interferometers and accessories.

The Pentax fish-eye zoom lens has a diagonal FOV varying between 180° at the wide end and 90° at the long end. The Birds-Eye lens forms a circular fish-eye image with FOV of 180° across the image circle. All other Fish-Eye lenses form full-frame images with a diagonal FOV equal to 180°.

GRINlens

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For a simple image comparison, a spherical lens can be seen as a cut of a sphere whereas an aspherical lens can be defined by more complex shapes, for example conic or elliptic.

Aspherical lens

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Convexlens

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The calculator below converts between the focal length f and the field of view (FOV) of a rectilinear lens. The formula that it implements is FOV = 2 arctan (x / (2 f)), where x is the diagonal of the film. The FOV is measured across the frame’s diagonal, and is therefore smaller across the horizonal dimension, and even smaller across the vertical dimension.

Until now all Pentax DSLRs use a sensor smaller than the standard 24 x 36 mm film frame. The lens still produces a 24 x 36 mm image, but the sensor only captures the central portion of that image — your wide-angle is not so wide and your tele is even longer. The calculator below takes the 1.5 x crop factor into account.

Cylindricallens

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An aspherical lens can be defined as a non spherical lens with at least a one optical face that can be defined following below conical equation.

Fresnellens

aspheric lenses中文

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The other solution to remove the spherical aberration is to design the shape of the lens to avoid it, these complex shapes are defined by conical equation and are defined as aspherical shapes. Manufacturing of aspheres is more complex, but with recent (last 20 years) digitalisation of the production and testing equipment it becomes easier and cheaper.

Lenticularlens

The difference between both lenses comes from their shape, while a spherical lens shape can be defined from a virtual center and a fix radius of curvature, an aspherical lens shape is defined from a virtual center point point but with different values of radius of curvature according to their relative angle.

Spherical lenses are easy to manufacture, but it has been identified by early opticians that using these lenses comes with aberrations on the image, called spherical aberrations. To compensate these aberration one can use doublets or complex systems of lens but this is costly and will take more space and weight.

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Improvement of production technology has brought a democratization of the use of complex aspherical lenses. What are their benefits, how to manufacture them, see our guide below for answers.