What is an f-theta lens?

F-theta lenses are the standard lenses for galvo-scanner-based laser marking, engraving, and cutting systems. The diffraction-limited, multiple-element, air-spaced lens design is optimized for a flat field in the image plane and low f-theta distortion.

What is f-theta distortion?

F-theta lens distortion F-theta lenses (used in laser scanning systems) are usually designed to produce a certain amount of distortion (barrel distortion) so that the image height is proportional to the field angle of θ.

What is the relation between tangential and sagittal focal length with angle of incident ray?

If there is some non-zero angle θ between the beam axis and the normal direction, the focal length is ftan = (R / 2) · cos θ in the tangential direction (i.e., within the plane of incidence) and fsag = (R / 2) / cos θ in the sagittal direction.

What is a 4f system?

Introduction. The 4f system is a commonly used optical relay that usually consists of two positive lenses with the input plane located one focal length (f1) in front of Lens 1 and the output plane located one focal length (f2) after Lens 2. The magnification is found to be equal to −f2∕f1.

How do telecentric lenses work?

Image-space telecentric lenses An image-space telecentric lens has the exit pupil at infinity and produces images of the same size regardless of the distance between the lens and the film or image sensor. This allows the lens to be focused to different distances without changing the size of the image.

What is the lens equation?

The lens equation allows us to understand geometric optic in a quantitative way where 1/d0 + 1/di = 1/f. The lens equation essentially states that the magnification of the object = – distance of the image over distance of the object.

How do you find the focal length when given the radius of curvature?

The relation between focal length (f) and radius of curvature (R) of a spherical mirror is that the focal length is equal to half of the radius of curvature i.e. f=R2.

What is 2f system?

2f systems reproduce only position and not vergence of ray bundles emerging from the object in the image plane and thus require converging light incident on the scanning mirrors to relay collimated light to the ocular pupil.

What is magnification in telecentric lens?

Telecentric lenses are designed to have a constant magnification regardless of the object’s distance or location in the field of view. This attribute is ideal for many machine vision measurement applications, as measurements of an object’s dimension will be independent of where it is located.

What is called as converging lens?

If parallel rays of light fall on a convex lens they converge when passing through and meet at a point on the other side. That’s why the convex lens is known as a converging lens.

What is the equation of a convex lens?

The equation of the convex lens s = do = the object distance, s’ = di = the image distance, ho = P P’ = the object height, hi = Q Q’ = the image height, F1 and F2 = the focal point of the converging lens. The P’AP triangle is similar to the Q’AQ triangle.

What are F Theta lenses used for?

F-Theta Lenses. F-theta lenses have been engineered to provide the highest performance in laser scanning or engraving systems. These lenses are ideal for engraving and labeling systems, image transfer, and material processing.

What is the theta-function solution to the heat equation?

This theta-function solution is 1-periodic in x, and as t → 0 it approaches the periodic delta function, or Dirac comb, in the sense of distributions. General solutions of the spatially periodic initial value problem for the heat equation may be obtained by convolving the initial data at t = 0 with the theta function.

What is the theta function used for in calculus?

The theta function was used by Jacobi to construct (in a form adapted to easy calculation) his elliptic functions as the quotients of the above four theta functions, and could have been used by him to construct Weierstrass’s elliptic functions also, since