Differential error is a variation in magnification between the left and the right sides of a comparison microscope. A substantial differential creates a systematic accuracy loss in the instrument that can reduce credibility in the courtroom. In legal systems where photos or measurements from a comparison are required during expert testimony or in case notes, a defense lawyer could argue that image overlays or air-gap caliper readings demonstrating a match are too inaccurate to be used if they come from a microscope with large differential error. In cases where the court requires re-examination of a specimen during the legal process, a large differential error can even lead to a different test result if a different microscope is used in the later test.
Magnification error is a phenomenon in which an object placed close to the objective appears to be larger than the same object placed farther away (Figure 2). This error is commonplace in microscopes using standard optics. It comes into play when comparing two objects that are not mounted at precisely the same distance from their objective lenses.
When using the air-gap method to measure features, magnification error between the specimen view and the caliper view reduces the accuracy of readings. When comparing a test-fired bullet to one gathered as evidence, magnification error can cause incorrect test results during a comparison by turning matching marks or patterns into an apparent non‐match. It also reduces reproducibility of results as the distance from the specimen to the lens varies between the initial test and subsequent ones.
Fig. 2: An example of magnification error using two dowels of same diameter but different height. Perspective view shows relative size (left). In top view of the same items (right), the taller dowel appears to be larger because it is closer to the lens.
Although zoom capability offers a convenient way to reduce magnification error, it comes at a large price. Zoom lenses are far more complicated than fixed lenses and are therefore more prone to error. The additional elements required for the zoom function increase the dimensional variations that occur during lens manufacturing. This can increase the differential error between the two sides of the comparison microscope by more than a factor of ten.
Offsetting magnification error by matching image sizes using a zoom function is manually done by humans, which introduces another source of inaccuracy. When comparing a tool feature to a mark on a specimen, by using zoom it is even possible to inadvertently make the two appear to be the same size when they really are not, leading to a false positive match.
Manual zooming also has a negative impact on reproducibility. Reproducibility is defined as the ability to return to the same settings for repeated tests and to reliably repeat an examination at a later date with the same results. Since it is routine for courts to request additional examinations well after the initial test, high reproducibility is key. The human variation in manual zoom-ing and the large differential errors in zoom lenses can lead to different results from the later test, particularly if a different microscope or operator is used. Reliably returning to the same test settings with manual zoom is also very difficult.
Parallax error (also known as perspective error) is caused by magnification error when view-ing objects that are highly three-dimensional or when comparing objects that are at different heights in the optical path. Points in the field of view that are vertically aligned in reality appear to no longer line up. This error is created when looking at the object from a non-perpendicular angle (Figure 3).
A common example in microscopy is the apparent movement of a reticule in an optical sight relative to the specimen when the user moves his/her head from side to side. The same effect can be seen when measuring features on a specimen by overlaying them with a caliper using a comparison microscope (if the caliper is mounted at a different height from the specimen). It can even occur when the caliper and specimen are mounted to the same stage if the feature being measured is held behind the caliper’s jaw edges instead of between them.
Fig. 3: Parallax error causing measurement inaccuracy. In left image, cartridge case is centered in field of view and on-screen measurement reads 4.62 mm from center of hole (far from objective) to edge of case (close to objective). In right image, same measurement is taken off-center and reading changes to 5.12 mm.
Parallax error also causes features that stand proud from the product’s surface to appear to lean away from the optical axis (the center of the field of view). The direction and magnitude of the apparent lean varies with the position of the feature within the field of view (Figure 4). This distortion makes reproducible testing difficult to achieve unless the sample is fixtured to be placed in exactly the same position each time.
With so many errors hidden in the optics of standard microscopes, it may seem impossible to reliably inspect anything requiring quantitative reporting. However, careful consideration of a microscope’s optical design can avoid this problem. For example, comparison microscopes are available with telecentric optics that eliminate or dramatically reduce inaccuracies and loss of reproducibility caused by differential error, magnification error, zoom and parallax.
Telecentric lenses have existed for decades, but through the 20th century were labeled as "exotic" and sidelined to fringe applications. The technology first gained widespread use in the last ten years with the expansion of machine imaging and vision-based quality control measure-ments in industrial manufacturing.
Telecentricity is a feature of an optical system in which all rays passing through the system are very nearly collimated and parallel to the optical axis. An optical system can be telecentric in the image space (the eyepiece/camera side), the object space (the objective side) or in both. Telecentricity is achieved by placing an optical stop (an opaque screen with a small hole in the center) at a focal point within the compound lens. The screen blocks all light except the narrow ray bundles which are collimated (or very nearly so) and parallel to the optical axis (Figure 5).
In simpler terms, when viewing an object through a telecentric lens, the viewer is looking "straight down" on all points in the field of view. In contrast, with non-telecentric optics the viewer looks straight down only at the very center of the field of view and at an angle at all off-center points.
Designing a microscope for telecentricity gives the system several optical properties that are highly beneficial for measurement accuracy, reduction of distortion and reproducibility of results.
The most important property of the telecentric optical system is constant magnification with varying distance between the specimen and the microscope objective. This concept can be difficult to grasp because we don’t see telecentrically. To the human eye, closer objects appear to be larger than ones further away. This works well for normal viewing, but when creating images of specimens which must be accurately compared, precisely measured and reliably repeated, constant magnification is crucial.
Constant magnification provides more accurate comparison of samples of different heights because the apparent size of the object does not change with its distance from the objective lens (Figure 6). It also enables more accurate measurement of complex 3-D shapes, such as a large tool whose surfaces are also at varying heights.
Fig. 6: Objects of same diameter at different distances from the lens (from Figure 2), as seen through standard camera optics (left) and telecentric camera optics (right).
When measuring features using the air-gap caliper method or a reticule, constant magnification ensures that the distance between points on a tall feature doesn’t appear artificially greater than the same distance on a low feature (such as a mark left at the bottom of a hole). It also provides better reproducibility when re-viewing a sample previously viewed at a different height.
A critical benefit of constant magnification is that it eliminates the need to zoom. Telecentric lenses in leading comparison microscopes today are fixed lens systems because they do not need zoom functionality in order to match the image sizes from both sides of the microscope. Excluding the zoom function allows simplification of the lens system and tighter manufacturing tolerances, which can reduce magnification differential errors to under 0.4 %. It also eliminates the human error introduced when using a zoom feature.
Fixed lenses are also more stable, with imperceptible drift even during temperature variations.
With telecentric optics, features on a sample can be accurately measured even if they are out of focus because objects that are not at the point of best focus blur symmetrically. This holds the centroid position constant and allows for accurate location of features and edges without distortion. This removes the requirement on the user to keep all points on the sample in simultaneous focus.
No parallax error (perspective error)
The elimination of parallax error is critical to achieving results that are both accurate and reproducible when examining specimens that are highly three‐dimensional (Figure 7), such as when observing or measuring small features at various points on a large tool and comparing to tool marks on a piece of evidence. Using telecentric optics ensures that the apparent shape, size and location of features on the object do not vary if the piece is moved to a different location in the field of view (or if the piece is removed and inspected again later at a different location).
Equal sightlines to all points in the field of view
With standard optics, the line of sight is perpendicular to the surface of the object only in the center of the field of view, with all other points viewed at an angle. This means that low-lying features that are not centered in the field of view can be hidden by neighboring tall features. Since telecentric optics are designed to look straight down at all points in the field of view, these problems are eliminated. This enables visualization of challenging points such as the inner diameters of two parallel tubes that are spaced far apart, or the bottoms of deep holes that are off the optical centerline (Figure 8).
Fig. 8: A comparison of views of challenging shapes as seen through standard optics vs. telecentric optics. Sightlines to the bottoms of the deep holes are partially obstructed by the top edges of the holes when viewed off-center with standard optics (left). When viewed with telecentric optics (right), the entire surface of the bottom of the hole is visible.
In addition to improving image quality, measurement accuracy and inspection reproducibility, choosing a microscope with telecentric optics also provides advantages when capturing images for documentation of results.
Sharpness of images
Today’s cameras no longer save images to film, but instead use a sensor array at the old film location to capture the image digitally. Imaging arrays perform best when light is normally incident on their surfaces because each sensor element’s construction has non‐zero thickness. Additionally, some arrays use color filters above each sensor element, which increases the effective thickness of the element. When light hits the array at an angle, as with standard optics, some of the light rays are blocked or distorted on their way to the sensors’ surfaces. This reduces the sharpness of the captured image and produces crosstalk between colors. Telecentric optics send all light to the sensing array at nearly zero angle of incidence, avoiding blurring and color crosstalk.
More uniform brightness of captured images
Since the incoming light is normally incident on the sensor array at all points, the image plane is uniformly illuminated. This avoids image files which appear brighter in the center and slightly darker at the edges.
Accommodates changes in placement of eye or camera
The constant magnification that is critical on the objective side is also important on the eyepiece side. With standard optics, changing the distance between the objective and the camera’s sensor array changes the size of the captured image. This reduces reproducibility of results if a different microscope is used or if the camera on the microscope is swapped. Additionally, if the two sides of a comparison microscope are focused differently a mismatch in lens distances is created. This introduces a magnification mismatch at the camera back. Optics that are telecentric on the image side provide constant magnification at the sensor array with varying distance from the objective, eliminating these problems. Cameras can be replaced and exchanged with-out compromising accuracy and reproducibility of results.
It is a common misunderstanding among users of equipment with telecentric optics that there is a software mechanism adjusting the image to achieve constant magnification and other error reductions. Although it is possible to do some of this, many of the advantages of telecentric lenses cannot be accurately reproduced by software.
Certification and calibration of optics
Another common misunderstanding in the microscopy community is that third-party certification of each microscope’s optics ensures inspection accuracy and reproducibility. In reality, governmental standards organizations typically certify calibration equipment but do not certify individual instruments.
Microscope manufacturers can perform internal calibrations on individual instruments, but here another disadvantage of zoom capability comes into play. After the initial calibration by the manufacturer, the variation introduced by the zoom setting makes it difficult to reproduce the calibration in the field.
Elimination of the zoom feature enables use of fixed optics, simplifying the lens configuration. This makes self-certification and calibration easy because there are no steps required to ensure that a zoom setting is correct.
Calibrations performed at the time of manufacture can help reproducibility by improving consistency of performance between microscopes made by the same supplier. However, no calibration can eliminate errors which are caused by fundamental optical principals of non-telecentric lenses such as parallax and non-constant magnification.
Optical systems in modern microscopy equipment can be subject to a variety of hidden errors. Careful consideration of the optical design used in the equipment is critical. Using microscopes with telecentric optical systems reduces or eliminates many of these errors to optimize image quality, measurement accuracy and reproducibility.