Modified Thin-Lens EquationThe incident and output light are assumed to propagate as Gaussian beams (Figure 2). The modified thin-lens equation was derived by relating the input and output beam properties (table, center) across the lens:

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Gaussian beam

While traditional optical comparators are generally straightforward to use, they present significant disadvantages to both users and clients. Some of the most significant drawbacks include:

Here we will discuss what comparators are, as well as the following questions: what is an optical comparator used for, how does it work, and how do traditional models compare to digital ones?

In another case, the conventional thin-lens equation predicts the image can be infinitely distant. But, if the beam is Gaussian with a nonzero Rayleigh range, the beam waist cannot be imaged to infinity. Instead, the maximum image beam waist distance,

Companies across a range of industries use digital optical comparators to solve various applications. Below are some common digital optical comparator uses and applications:

Gaussian beampropagation simulation

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Although these limitations present no issues for non-repetitive tasks used to analyze 2D parts, anything outside of this defined operating bubble is an obstacle for traditional optical comparators. For large-scale, complex analysis, a different model is necessary.

depends on the Rayleigh range of the input beam. For the image beam waist to appear at this distance, the object beam waist should be separated from the lens by a distance one Rayleigh range larger than the focal length, ().

Manufacturing companies need tools that are quick and easy to use to handle large quantities of complex parts. This is where digital optical comparators come into play. Digital optical comparators take the concept of traditional optical comparators and apply new technology to key areas. The result is an automated technology that is faster and easier to use, reducing the labor input of operators.

The modified thin-lens equation also includes either the input Rayleigh range (zR ) or the output Rayleigh range ( zR '). The Rayleigh range (Rayleigh length) is measured starting at the beam waist, along the propagation direction, to the point where the beam radius is larger by a factor of √2. Highly divergent beams have short Rayleigh ranges.

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Profile projectors are generally straightforward and require little training to use. Traditional optical comparators that use silhouette measurement or point comparison simply require the user to fix a part in place and observe the on-screen image.

The optical comparator (profile projector) has been used in quality control in the manufacturing industry since it was first patented in 1925. The overall design has changed little in that time, with the exception of some digital and software enhancements. The continuing popularity of this device is a statement of how useful it is for optically checking parts for conformance and deformities.

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Figure 3: Gaussian beam parameters such as the radius, W(z), and the wavefront's radius of curvature, R(z), are calculated using a distance, z, referenced to the beam's waist. The waist is always located at the origin.

This is the process used for most traditional optical comparators, though there are various methods available for this technology. For example, instead of an overlay with a part plan, an overlay may feature a grid or concentric circles to allow for more precise measurements of a part. Alternatively, a point comparison method may be used, where the image’s silhouette is centered on the screen compared to an overlay. The user then moves the stage to hit prescribed points on the overlay, measuring how much the stage had to move to match the part to each point.

Using an optical comparator doesn’t need to require extensive training or massive labor inputs. Simplify your optical inspection with VISIONx, Inc’s VisionGauge® Digital Optical Comparator. Our digital optical comparator is an advanced optical analysis tool that maximizes the function of optical comparator technology. They are extremely precise yet easy to use, delivering fast, high-quality results. They allow you to carry out fast and accurate inspections and measurements of parts, completely operator-independent.

In short, traditional optical comparators require extensive training to use properly and need significant labor input. While these limitations may be a non-issue for small operations that work with simple parts, the manufacturing industry as a whole is quickly growing in scale and complexity. It needs optical comparator tools that can keep up.

Objects, and Images, and Laser BeamsThe conventional thin-lens equation (table, top) is based on the ray optics model and uses the focal length (f ) of the lens to relate the distance (s ) between the lens and the object to the distance (s ') between the lens and the image.

Where traditional optical profile projectors fall short, digital models pick up the slack. Manual comparator technology is highly useful in small-quantity applications, but with the rise of more complex parts and large-scale manufacturing, automation is necessary. Digital optical comparators present the solution.

So what does this mean for operators? Essentially, digital optical comparator instructions for operators are pared down from three steps to one: place the part on the staging area. From there, the digital optical comparator does the rest. The system will automatically handle alignment and comparison, providing a pass/fail result along with analytical data supporting the decision.

Note that the beam radius (W ) and wavefront's radius of curvature (R ) are calculated using the relative distance (z ) from the waist (Figure 3). There are two modifed thin-lens equations (table, bottom), since the form of the equation differs depending on whether the input beam parameters (zR and s ) or the output beam parameters (zR ' and s ') are known.

For example, the conventional thin-lens equation (see table), predicts the image will appear at infinity when the object is placed at the lens' front focal point. However, for Gaussian beams, when the object beam waist is one focal length away from the input side of the lens, the image beam waist is one focal length away from the output side.

The first two methods are used by traditional optical comparators and are the most common in the industry. The third is employed by digital optical comparators, which handle the entire process electronically.

Optical comparators, also called comparators or profile projectors, are measurement tools used in the manufacturing industry. Comparators inspect, measure, and compare the dimensions of manufactured parts. These measurement tools function using the principles of optics by utilizing illumination, lenses, and mirrors to project a magnified silhouette of a part upon a screen. Doing this compares the part to its prescribed limits.

Gaussian beamq parameter

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Figure 2: Key to the model are the relationships between the input and output beams at the lens. There, the beams have equal radii, and the beams' wavefront curvatures are related by the focal length of the lens. The wavefront' radius of curvature is flat (thick vertical line) at the waist and gradually becomes more spherical with increasing distance from the waist.

Gaussian beamdivergence angle

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If the laser beam is not perfectly Gaussian, its Rayleigh range will be shorter than the Rayleigh range of an ideal Gaussian beam with the same waist radius. The ratio of the two values, M2 (M-squared), is often specified for laser beams. Multiply the beam's Rayleigh range by the M2 value, and then use this product as zR or zR ' in the modified thin-lens equation to find s ' or s , respectively.

Digital optical comparators pick up the slack where traditional models fall short. Digital optical comparators, like traditional models, utilize optics for comparing a part to its plans. However, digital optical comparators do so by augmenting the existing comparator technology with a combination of measurement and analysis tools. Digital optical comparators directly reference CAD drawings of parts for comparison, along with laser measurement tools and advanced comparison software.

Optical comparators of both types can be found in manufacturing shops and lab environments related to quality control. They are most popular in industrial sectors, including the scientific, automotive, medical manufacturing, aerospace, and defense industries.

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In the modified thin-lens equation, these distances refer to the separations between the lens and the input and output beam waists, respectively (Figure 1). The radius of a beam is smallest at its waist and increases with distance. A lens placed in the beam outputs a new beam with its own waist and divergence characteristics. The input beam waist radius (Wo ) is treated as the object size, and output beam waist radius (Wo' ) as the image size.

Field of view (FOV) is the maximum area of a sample that a camera can image. It is related to two things, the focal length of the lens and the sensor size.

Another way that optical comparators differ is in the measuring processes they use. There are three different measuring processes for comparators:

While automation is one of the many significant benefits to using the VisionGauge® Digital Optical Comparator, the system is also accurate and efficient when used manually by an operator wanting to perform direct measurements on a part or make manual comparisons of a part to its CAD file. The VisionGauge® software interface is intuitive and easy-to-use even for manual operation: Operators can quickly load part CAD files and pre-programmed inspection routines with the system’s barcode reader, and the stages and overlay can be manually controlled with the system’s industrial-grade joysticks. Both automated and manual operation modes produce highly accurate results and complete documentation.

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Optical comparators use this same principle. A part is affixed to a stage and a light source shines on it, resulting in a shadow image of the part. The shadow is magnified with lenses and bounced by mirrors onto the back of a screen. This screen is fixed at a known distance for measurement purposes.

Laguerre-Gaussian mode

In the case of laser light, a modified thin-lens equation that takes diffraction into account is recommended instead of the conventional thin-lens equation. The modified equation, which models the laser light as Gaussian beams, is appropriate for many single-mode and fiber-coupled laser sources. In addtion, the equation can be adapted for use when the laser light does not have a perfect Gaussian intensity profile. [1]

Optical comparators are used to check for both dimensional accuracy and surface defects, such as scratches and indentations. In short, they allow for non-contact measurement and observation, minimizing handling while still allowing for close inspection.

laguerre-gaussianbeam

While traditional optical comparators are easy to use and operate, they also present disadvantages because of their simplicity. Some primary flaws of traditional optical comparators include the following:

Figure 1: A thin lens, with focal length f , is shown inserted in a Gaussian beam. In the modified thin-lens equation, the object is the input beam's waist, located a distance s  from the input side of the lens. The input beam's radius (W ) is Wo at its waist and maintains a similar radius over the Rayleigh range (±zR ). The image is the output beam's waist, located a distance s ' from the lens' output side. The output beam's radius (W ') is Wo' at its waist and remains nearly Wo ' over its Rayleigh range (±zR').

Gaussian beamcalculator

Optical comparators can vary in the size and magnification of the projected image. Both of these metrics depend on the optics and screen size of the comparator. Screen sizes for optical comparators range from 12 to 36 inches, though models with larger screens are available. However, larger screen sizes are only possible with larger enclosures, as a greater distance is required to generate a bigger image without distortion.

Unique Behavior of Gaussian BeamsThe behavior of Gaussian beams can be surprising, especially when compared with the predictions of the ray optics model and the conventional thin-lens equation.

Optical comparators have changed little since they were invented in the 1920s — the reason for this is that the technology uses optics, which have only changed in quality, not function. Optical profile projectors work similarly to overhead projectors commonly used in classrooms. A light is directed through a stage to a series of lenses and mirrors, which then project the silhouette of whatever is on the stage onto a screen.