It’s a somewhat more advanced and complex microscopy concept, since it takes into account the tilt and tip of the space between the image plane and the objective lens sensor plane. It’s also affected by aberrations and diffraction figures extending above and below the image plane.

Use of multiple filters, each of which prevent the passage of light waves at different orientations, allows finer attenuation of light. A filter only allowing vertical light to pass, followed by a filter only allowing horizontal light to pass, would act together to block most of the light waves passing through the filter pair.

When it comes to image resolution or the clarity of detail of a specimen’s magnified image, this is typically inversely proportional to the numerical aperture, and therefore directly proportional to the depth of field.

Where, d is the depth of field, λ is the wavelength of the light from the light source, n is the refractive index of the medium between the specimen and the objective lens, and NA is the numerical aperture of the objective lens.

What is depth of field microscopeformula

The working distance of the objective lens also has an effect on the depth of the field. A short working distance results in a smaller depth of field, while a longer working distance, as when focusing at the farthest point from the lens, creates a higher depth of field where almost everything before that point is in focus.

In relation to resolution is the contrast of the specimen and its magnified image. Different resolutions and contrasts have different corresponding depths of field. Smaller specimen details require a higher spatial frequency, and results in a smaller depth of field, while a lower contrast benefits from a higher depth of field.

Similarly, in machine vision, artificial polarization techniques help developers select or restrict the direction of the light waves that enter a camera lens and strike an image sensor. The three basic ways to artificially polarize light are linear polarization, circular polarization, and elliptical polarization, with the latter two methods serving as extensions of linear polarization and not widely used in machine vision.

Where d is the depth of field, λ is the wavelength of the illuminating light, n is the refractive index of the medium, NA is the numerical aperture of the objective lens, M is the lateral magnification of the lens, and e is the smallest resolvable distance of a detector on the image plane.

The proper way to employ polarization in an inspection environment typically involves polarizing both the light source and the reflected light (Figure 3) with a polarizer placed at the source of the light, at an angle that benefits the application, and a second polarizer placed at the same or a complementary angle, onto the lens of the camera conducting the inspection.

Knowing the depth of field of the microscope at any given setting is important since it affects how much you have to move the specimen slide up, down, left, or right to image certain areas of the specimen, especially since it determines the required stability of the focusing axis.

Polarization techniques Returning to the example of the sun reflecting off the surface of water and producing glare, a photographer may employ a polarization filter to remove that glare, improving the image by filtering light at the specific angle causing the glare. Similarly, in machine vision, artificial polarization techniques help developers select or restrict the direction of the light waves that enter a camera lens and strike an image sensor. The three basic ways to artificially polarize light are linear polarization, circular polarization, and elliptical polarization, with the latter two methods serving as extensions of linear polarization and not widely used in machine vision. Dichroic, thin-film, and wire-grid polarizers represent the most common components used in machine vision to linearly polarize light. Wire-grid polarizers specifically can withstand the power levels of lasers, which can be useful in factory and scientific environments. Polarization filters function by selecting or restricting light waves traveling in a single plane. The orientation of the filter determines the orientation of the light waves that can pass through the filter, thereby selecting one set of light waves to advance and preventing others from continuing (Figure 2). Use of multiple filters, each of which prevent the passage of light waves at different orientations, allows finer attenuation of light. A filter only allowing vertical light to pass, followed by a filter only allowing horizontal light to pass, would act together to block most of the light waves passing through the filter pair.

Common polarization techniques in machine vision include inspection of glass and highly reflective materials. Raw and machined metal have grain at a microscopic level that can lead to linear polarization, making the use of a polarization filter useful. Plastic and glass, automotive, packaged materials, semiconductor, and LCD inspection applications commonly make use of polarization filters.

The dynamic process allows for the correction of glare that may originate from different angles on individual items to be inspected, making it easier to extract features, scratches, or even to see material stress in plastic.

The numerical aperture of the objective lens is the main factor that determines the depth of field. In this sense, the microscope’s depth of field and depth of focus are somewhat similar, since these both generally increase as the numerical aperture is decreased.

With more than 35 years of experience, David Dechow is the founder and owner of Machine Vision Source (Salisbury, NC, USA), a machine vision integration firm. He has been the founder and owner of two successful machine vision integration companies. He is the 2007 recipient of the AIA Automated Imaging Achievement Award honoring industry leaders for outstanding career contributions in industrial and/or scientific imaging.

The general rule is that depth of field is inversely proportional to the numerical aperture, which is the size of the opening of an optical component where light passes through- in this case, the objective lens. So, a high numerical aperture results in a low depth of field, and vice versa.

Understanding the growing list of polarization applications requires a discussion of the latest polarization cameras and sensors and an understanding of the benefits and limitations associated with the use of polarization technology.

Light is a transverse wave, i.e. its electromagnetic and magnetic fields are disturbed at right angles relative to the direction of travel of the light waves. Or, it can be said that light waves oscillate perpendicular to their direction of travel.

By interpolating the images from each four-pixel block, the sensor gathers considerable information about the linear polarization occurring on the surface of the object being viewed. These interpolated pixels allow a very accurate definition of the exact direction and intensity of the polarization within each four-pixel group.

It is the axial or longitudinal resolving power of the objective lens, measured parallel to the optical axis. This number is largely determined by the numerical aperture of the objective lens, and is considerably small that it’s typically measured in microns.

This is because the distance between the angular resolution of the lens and the two intersecting points of the light path coming through the aperture are what determines the range of the depth of field.

Dechow is a regular speaker at conferences and seminars worldwide, and has had numerous articles on machine vision technology and integration published in trade journals and magazines. He has been a key educator in the industry and has participated in the training of hundreds of machine vision engineers as an instructor with the AIA Certified Vision Professional program.

Polarization filters function by selecting or restricting light waves traveling in a single plane. The orientation of the filter determines the orientation of the light waves that can pass through the filter, thereby selecting one set of light waves to advance and preventing others from continuing (Figure 2).

The sky is blue because sunlight strikes the molecular structure of the atmosphere and scatters, which polarizes the light in a specific direction. As the angle of the sun relative to the atmosphere changes the polarization angle of the light also changes, and the human eye perceives color changes from dawn to midday to dusk.

The depth of field is defined as the distance between the nearest and farthest object planes that are both in focus at any given moment. In microscopy, the depth of field is how far above and below the sample plane the objective lens and the specimen can be while remaining in perfect focus.

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Field ofviewmicroscope

An important concept in microscopy is the depth of field, and the depth of focus, which are two related principles that are often interchangeably used. Both of these things have to do with the range of distance where the image is clear and in focus.

The average depth of field at certain magnifications and apertures is 3 to 5 microns at 4x magnification, 0.5 microns at a 0.8 numerical aperture, and 0.1 to 0.2 microns at a 1.47 numerical aperture.

The IMX250MZR/MYR (monochrome/color) Polarsens sensor from Sony (Tokyo, Japan; www.sony.com) represents a recent implementation of on-sensor polarization technology. The polarization elements are fabricated right into the silicon, under the microlens (Figure 4), which makes the sensor unique. In the color sensor, color filters are located directly underneath the polarizers.

At this range, advanced auto-focus systems such as laser trackers are essential, since manual focusing is almost impossible to achieve.

Depth offocus formula

Having said that, since the depth of field concerns the objective lens, there are a few other factors that must also be taken into account.

Whathappens to thedepth of fieldas total magnification decreases

Below is a detailed explanation of what the depth of field and depth of focus are, the different factors that affect the depth of field, and how to calculate it.

The polarizers in Sony’s sensor, a microscopic implementation of a wire-grid polarizer over every lens on the sensor, have 0°, 45°, 90°, and 135° polarization angles in four-pixel groups. The groups are interpolated, reducing the sensor’s overall functional resolution by 4x. In other words, each four-pixel block equates to one pixel of output.

Placing a polarizer only over the camera lens, and thus only polarizing the light reflecting off the object to be inspected, may sometimes be an effective technique but far more often not. To demonstrate the point, consider the example of photography.

A polarizing image sensor makes a polarization filter part of the image sensor, versus a separate component placed over the sensor. The Photron Crysta by Photron (San Diego, CA, USA; www.photron.com) and PolarCam from 4D Technology (Tucson, AZ, USA; www.4dtechnology.com), to cite two examples, have been in the marketplace for some time and make use of on-sensor polarization.

The depth of field is inversely proportional to the numerical aperture of the objective lens, directly proportional to resolution, contrast, and working distance, and is also affected by magnification.

Even if the light projected onto an object is polarized in order to limit the potential number of reflective polarization angles, the reflective properties of the object may still create unwanted polarization when the light reflects off the object. Employing two filters allows for finer control of the light angles that enter the camera, ensuring the desired crispness of the image.

Dichroic, thin-film, and wire-grid polarizers represent the most common components used in machine vision to linearly polarize light. Wire-grid polarizers specifically can withstand the power levels of lasers, which can be useful in factory and scientific environments.

Returning to the example of the sun reflecting off the surface of water and producing glare, a photographer may employ a polarization filter to remove that glare, improving the image by filtering light at the specific angle causing the glare.

New technologies and components A polarizing image sensor makes a polarization filter part of the image sensor, versus a separate component placed over the sensor. The Photron Crysta by Photron (San Diego, CA, USA; www.photron.com) and PolarCam from 4D Technology (Tucson, AZ, USA; www.4dtechnology.com), to cite two examples, have been in the marketplace for some time and make use of on-sensor polarization. The IMX250MZR/MYR (monochrome/color) Polarsens sensor from Sony (Tokyo, Japan; www.sony.com) represents a recent implementation of on-sensor polarization technology. The polarization elements are fabricated right into the silicon, under the microlens (Figure 4), which makes the sensor unique. In the color sensor, color filters are located directly underneath the polarizers. The polarizers in Sony’s sensor, a microscopic implementation of a wire-grid polarizer over every lens on the sensor, have 0°, 45°, 90°, and 135° polarization angles in four-pixel groups. The groups are interpolated, reducing the sensor’s overall functional resolution by 4x. In other words, each four-pixel block equates to one pixel of output.By interpolating the images from each four-pixel block, the sensor gathers considerable information about the linear polarization occurring on the surface of the object being viewed. These interpolated pixels allow a very accurate definition of the exact direction and intensity of the polarization within each four-pixel group.

Polarization techniques can also be deployed in line scan cameras like the quad-linear Piranha4 from Teledyne DALSA (Waterloo, ON, Canada; www.teledynedalsa.com), which has four linear sensor lines, each of which has an on-sensor polarizer, with each sensor line set to a different polarization angle.

The depth of focus is determined by both the numerical aperture or sensor size and the magnification of the objective lens, and is also, in a way, related to the resolution.

Depth offocus in optics

We have provided a general formula above for calculating the depth of field of the microscope, and this works perfectly well for low to average magnification lenses. But, there is actually another formula that is especially for high magnification optics.

Applications and implementation Common polarization techniques in machine vision include inspection of glass and highly reflective materials. Raw and machined metal have grain at a microscopic level that can lead to linear polarization, making the use of a polarization filter useful. Plastic and glass, automotive, packaged materials, semiconductor, and LCD inspection applications commonly make use of polarization filters. The proper way to employ polarization in an inspection environment typically involves polarizing both the light source and the reflected light (Figure 3) with a polarizer placed at the source of the light, at an angle that benefits the application, and a second polarizer placed at the same or a complementary angle, onto the lens of the camera conducting the inspection. Even if the light projected onto an object is polarized in order to limit the potential number of reflective polarization angles, the reflective properties of the object may still create unwanted polarization when the light reflects off the object. Employing two filters allows for finer control of the light angles that enter the camera, ensuring the desired crispness of the image. Placing a polarizer only over the camera lens, and thus only polarizing the light reflecting off the object to be inspected, may sometimes be an effective technique but far more often not. To demonstrate the point, consider the example of photography. The polarizers used by photographers rotate, to allow the photographer to attune the polarizer to the precise angle at which the light is being polarized by the surface of the subject in the scene. The photographer tunes the angle of polarization as needed for different scenes, not a practical technique for automated imaging in machine vision. Take, for example, parts on a conveyor belt rapidly passing underneath a camera for inspection. It’s impossible to achieve perfect, replicable results during parts inspection, even with polarized light and filter working in concert, because there will likely be variances in the position of objects relative to the camera, which affects the angles at which polarized light reflects off the surface of the object. However, a new technology and new components becoming readily available overcome the limitation.

Each line in a time delay integration (TDI) setup is successively struck with each of the four polarization angles (Figure 6). The four images then combine into a composite image, providing a full-resolution polarization image, versus the four-pixel interpolated image created by an area sensor like the IMX250MZR/MYR.

Polarization - Definition of Concepts, Techniques, and TechnologiesPolarization, a filtering technique used for decades by photographers for image enhancement, also sees widespread use in commercial applications, including machine vision image acquisition. With polarizing cameras and imaging components increasingly entering the vision application mainstream since 2018, new applications and uses for polarization in machine vision continue to emerge. Understanding the growing list of polarization applications requires a discussion of the latest polarization cameras and sensors and an understanding of the benefits and limitations associated with the use of polarization technology.Polarization concepts Light is a transverse wave, i.e. its electromagnetic and magnetic fields are disturbed at right angles relative to the direction of travel of the light waves. Or, it can be said that light waves oscillate perpendicular to their direction of travel. Natural light, and virtually all artificial light (LEDs, incandescent lights, fluorescent lights, etc.) is unpolarized or weakly polarized. Natural light travels in any radial direction from the source of the light (Figure 1). Imagine a beam of light. Light waves oscillate 360° from every point along that beam. (An oversimplification, to illustrate the concept.) Polarized light, on the other hand, is light in which the waves travel in only one, specific direction. Light can be polarized in nature by absorption, refraction, reflection, scattering, and birefringence (double refraction). For example, when light strikes water, it can be reflected linearly perpendicular, i.e. polarized in that specific direction, to the surface of water, which we experience as glare. For another example, as the sun moves across the sky the angle of the sun’s light striking a window will change. At some point the light will reflect off the window, or be polarized, at an angle perceived as glare. The sky is blue because sunlight strikes the molecular structure of the atmosphere and scatters, which polarizes the light in a specific direction. As the angle of the sun relative to the atmosphere changes the polarization angle of the light also changes, and the human eye perceives color changes from dawn to midday to dusk.

Depth offocus definition

On-chip polarization sensors, now available to virtually any camera manufacturer, drive advances in software and solutions that developers and manufacturers provide for machine vision systems. An increasing number of viable polarization applications can now be expected.

The polarizers used by photographers rotate, to allow the photographer to attune the polarizer to the precise angle at which the light is being polarized by the surface of the subject in the scene. The photographer tunes the angle of polarization as needed for different scenes, not a practical technique for automated imaging in machine vision.

Depth of field microscopethreads

Hence, arguably the best way to calculate the depth of field is by combining both wave and geometrical optical depths of field.

DOLP, or degree of linear polarization (the intensity and direction of linear polarization as it’s interpreted from the four angles of each four-pixel group), and AOLP, or angle of linear polarization, (the angle of the light as it reaches the sensor plane) can be adjusted. Adjusting these parameters allows fine control of polarization similar to how a photographer rotates their polarization filter to achieve the desired crispness of image (Figure 5).

As such, there is a higher chance of making an error in focusing an image at higher magnifications, making the depth of field immensely important for thick and irregularly shaped objects with complex geometries or a variety of high and low surface points.

Depth of fieldvsdepth offocusmicroscope

In terms of magnification, this also has an influence on the depth of field of the microscope, especially when it comes to high magnification lenses, such as oil immersion lenses. Here, the depth of focus may be high, but the depth of field may below.

Natural light, and virtually all artificial light (LEDs, incandescent lights, fluorescent lights, etc.) is unpolarized or weakly polarized. Natural light travels in any radial direction from the source of the light (Figure 1). Imagine a beam of light. Light waves oscillate 360° from every point along that beam. (An oversimplification, to illustrate the concept.)

No technology provides a global cure for imaging challenges, however. Polarization is another tool in the toolbox of a vision system designer or integrator.

Polarization, a filtering technique used for decades by photographers for image enhancement, also sees widespread use in commercial applications, including machine vision image acquisition. With polarizing cameras and imaging components increasingly entering the vision application mainstream since 2018, new applications and uses for polarization in machine vision continue to emerge.

This is because the two are governed by different principles, where the phenomenon of circles of confusion governs low magnification, and high magnification is governed by the principles of wave optics.

While the depth of field refers to the object space, or the quality of the image coming from a stationary lens as the specimen is being repositioned, depth of focus talks about the image space, or the ability of the sensor to retain the focus of the image as the sensor changes positions.

Software can then dynamically handle the selection of either individual wave angles, or the computational manipulation of the variety of wave angles, to analyze the image in ways that only were possible previously by providing sets of filters, multiple images, or even multiple sensors, to acquire multiple polarized analyses of the individual image, itself.

For another example, as the sun moves across the sky the angle of the sun’s light striking a window will change. At some point the light will reflect off the window, or be polarized, at an angle perceived as glare.

Take, for example, parts on a conveyor belt rapidly passing underneath a camera for inspection. It’s impossible to achieve perfect, replicable results during parts inspection, even with polarized light and filter working in concert, because there will likely be variances in the position of objects relative to the camera, which affects the angles at which polarized light reflects off the surface of the object. However, a new technology and new components becoming readily available overcome the limitation.

Polarized light, on the other hand, is light in which the waves travel in only one, specific direction. Light can be polarized in nature by absorption, refraction, reflection, scattering, and birefringence (double refraction). For example, when light strikes water, it can be reflected linearly perpendicular, i.e. polarized in that specific direction, to the surface of water, which we experience as glare.