Thin lenses can be converging or diverging. Converging lenses are thicker in the middle than near the edges, and diverging lenses are thicker near the edges than in the middle. A thin lens has two focal

The thin-lens equation and the lens maker’s equation are broadly applicable to situations involving thin lenses. We explore many features of image formation in the following examples.

Haidinger's brushes

These cameras make use of light polarization to reveal hidden material properties and provide new possibilities for image processing by detecting and filtering different angles of light polarization when reflected, refracted, and scattered from an object.

Let xo denote the perpendicular distance of the object from the centerline of the lens and let xo be positive. Let xi denote the perpendicular distance of the image from the centerline of the lens. Then xi can be found from the lens equation

The incident ray, or an extension of the incident ray, must pass through f. For a converging lens draw the incident ray or its extension through the focus on the incident side, and for a diverging lens draw the incident ray so that its extension passes through the focus on the exit side. The intersection of the two rays marks the position of the image. To check the accuracy of your drawing, draw a third ray through the center of the lens. This ray is not bent. It should pass through the intersection of the other rays that you have drawn.

Xo is positive for an object in front of the lens. Xi is positive if xo and xi are on the opposite sides of the lens. Xi is negative if xo and xi are on the same side of the lens. F is positive for a converging lens. F is negative for a diverging lens. The magnification is M = -xi/xo. If M is negative, the image is inverted. We can find the position and size of the image geometrically. Only two rays must be drawn.

Polarized visionoctopus

Do you want to know more about the potential of polarized light, how polarized cameras work and when you should select a polarized camera rather than a classic mono or color camera?

Polarizedsunglasses

Mono and color cameras can detect the light intensity and wavelength, which in case of glare or complex object textures is not enough for inspection or measurement.

After the webinar, each participant will receive the training material consisting of the .pdf presentation and a private link to the video recording on Vimeo.

Reducing glare effects, highlighting an edge position, or even knowing how different materials change the properties of light is an important advantage that can be the game changer for complex projects.

One of the challenges that machine vision has always faced is the inspection of low-contrast images and highly reflective samples.

axis between the two surfaces of the lens) that is negligible compared to the radii of curvature of the lens surfaces. Lenses whose thickness is not negligible are sometimes called thick lenses.

This webinar will cover all these topics. We will guide you through the world of light polarization, the physics laws behind this phenomenon, how polarized sensors mounted on industrial cameras work, the image processing performed on a polarized image, and how to choose between a polarized setup or a classic setup.

middle. A thin lens has two focal points, located on the optical axis, a distance f from the center of the lens on either side of the lens. Rays parallel to the optic axis passing through a thin converging lens come together at the focus f on the opposite side of the lens, and rays parallel to the optic axis passing through a diverging lens diverge as if they were leaving the focus on the incident side on a straight line path.

Mantis shrimpvision

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Consider a thin converging lens. Where does the image form and what type of image is formed as the object approaches the lens from infinity? This may be seen by using the thin-lens equation for a given focal length to plot the image distance as a function of object distance. In other words, we plot

A plane through a focus perpendicular to the optic axis is called a focal plane. Parallel rays converge in the focal plane or diverge from the focal plane, independent of the angle they make with the optic axis. Thin lenses can form real and virtual images.

IMAGE FORMATION BY THIN LENSES We use ray tracing to investigate different types of images that can be created by a lens. In some circumstances, a lens forms a real image, such as when a movie projector casts an image onto a screen. In other cases, the image is a virtual image, which cannot be projected onto a screen. Where, for example, is the image formed by eyeglasses? We use ray tracing for thin lenses to illustrate how they form images, and then we develop equations to analyze quantitatively the properties of thin lenses.

Draw the optical axis and the centerline of the lens. Mark the position of the foci. Draw the object in front of the lens. Draw an incident ray parallel to the optical axis from a point on the object to the centerline of the lens, and a refracted ray from the centerline through f. For a converging lens draw the refracted ray through the focus on the exit side, and for a diverging lens draw the refracted ray so that its extension passes through the focus on the incident side. Draw a second incident ray through f, and a refracted ray parallel to the optical axis.

The thin lens approximation ignores optical effects due to the thickness of lenses and simplifies ray tracing calculations. It is often combined with the paraxial approximation in techniques such as ray transfer matrix analysis. A single spherical interface between two transparent media can lead to image formation. But viewing these images is not always possible. Consider an air-glass interface. When the object is on the air side, the image can only be viewed from inside the glass. Giving the glass a finite thickness and adding a second spherical interface between glass and air will produce an image that can be viewed by someone in air. A piece of glass of finite thickness with two spherical boundaries is a lens. If the