Microscope Objectives for Life Sciences, Dry

Objective Tutorial

This tutorial describes features and markings of objectives and what they tell users about an objective's performance.

Objective Class and Aberration Correction

Objectives are commonly divided by their class. An objective's class creates a shorthand for users to know how the objective is corrected for imaging aberrations. There are two types of aberration corrections that are specified by objective class: field curvature and chromatic aberration.

Field curvature (or Petzval curvature) describes the case where an objective's plane of focus is a curved spherical surface. This aberration makes widefield imaging or laser scanning difficult, as the corners of an image will fall out of focus when focusing on the center. If an objective's class begins with "Plan", it will be corrected to have a flat plane of focus.

Images can also exhibit chromatic aberrations, where colors originating from one point are not focused to a single point. To strike a balance between an objective's performance and the complexity of its design, some objectives are corrected for these aberrations at a finite number of target wavelengths.

Five objective classes are shown in the table to the right; only three common objective classes are defined under the International Organization for Standards ISO 19012-2: Microscopes -- Designation of Microscope Objectives -- Chromatic Correction. Due to the need for better performance, we have added two additional classes that are not defined in the ISO classes.

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A cover glass, or coverslip, is a small, thin sheet of glass that can be placed on a wet sample to create a flat surface to image across.

The most common, a standard #1.5 cover glass, is designed to be 0.17 mm thick. Due to variance in the manufacturing process the actual thickness may be different. The correction collar present on select objectives is used to compensate for cover glasses of different thickness by adjusting the relative position of internal optical elements. Note that many objectives do not have a variable cover glass correction, in which case the objectives have no correction collar. For example, an objective could be designed for use with only a #1.5 cover glass. This collar may also be located near the bottom of the objective, instead of the top as shown in the diagram.

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The graph above shows the magnitude of spherical aberration versus the thickness of the coverslip used for 632.8 nm light. For the typical coverslip thickness of 0.17 mm, the spherical aberration caused by the coverslip does not exceed the diffraction-limited aberration for objectives with NA up to 0.40.

Telecentric Lenses

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 dimensions will be independent of where it is located.

Types of Telecentric Lenses
In order to achieve a telecentric lens design, all of the chief rays (rays from an off-axis point that pass through the center of the aperture stop) have to be parallel to the optical axis in either image space or object space, or both.

For an object space telecentric lens, the chief rays will be parallel to the optical axis on the object's side of the lens (object space). This is accomplished by setting the aperture stop at the front focal plane of the lens, which results in an entrance pupil at infinity. Since chief rays are directed towards the center of the entrance pupil, the chief rays on the object side of the lens will be parallel to the optical axis. An example of an object space telecentric lens is shown in Figure 1.

For an image space telecentric lens, the chief rays will be parallel to the optical axis on the image's side of the lens (image space). This is accomplished by setting the aperture stop at the back focal plane of the lens, which results in an exit pupil at infinity. Since the chief rays must pass through the center of the exit pupil, the chief rays on the image side of the lens must be parallel to the optical axis. An example of an image space telecentric lens is shown in Figure 2.

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Figure 1: A ray trace through an idealized object space telecentric lens system. Note that the chief rays (the center ray of each color) are parallel to the optical axis in object space, but in image space, the chief rays form an angle with the optical axis.

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Figure 2: A ray trace through an idealized image space telecentric lens system. Note that the chief rays (the center ray of each color) are parallel to the optical axis in image space, but in object space, the chief rays form an angle with the optical axis.

For a double telecentric, or bi-telecentric, lens, the front and back focal planes are made to overlap so that the aperture stop is located where both the entrance and exit pupils are at infinity. In a bi-telecentric lens, neither the image or object location will affect the magnification. Thorlabs' telecentric lenses are all bi-telecentric designs. Figure 3 shows an example ray trace through a bi-telecentric lens and illustrates how the chief rays pass through the system.

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Figure 3: A ray trace through an idealized bi-telecentric lens system. Note that the chief rays (the center ray of each color) are parallel to the optical axis in both image and object space, which means that the magnification will remain constant regardless of object distance.

Conventional Lenses
In conventional lenses, the entrance and exit pupils are not located at infinity, so the chief rays will not be parallel to the optical axis. In this case, the magnification of the object depends on its distance from the lens and its position in the field of view. Figure 4 above shows an example ray trace through a conventional camera lens; notice how the chief rays are angled with respect to the optical axis in both image and object space. Note that both Figures 3 and 4 feature the same lens design; only the aperture stop location was varied to shift the bi-telecentric system to a non-telecentric one.

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Figure 4: A ray trace through an idealized conventional camera lens system. Note that the chief rays (the center ray of each color) are not parallel to the optical axis in both image and object space, which means that the magnification will vary with object distance.

Example Images
Figures 5 and 6 show photographs taken with a bi-telecentric lens and a standard camera lens, respectively. With the telecentric imaging system, the height of the two screws appears to be the same, even though the object planes are separated by approximately 45 mm along the optical axis. With the conventional imaging system, the two screws appear to be different heights, which could result in inaccurate dimensional measurements. A machine vision system using a bi-telecentric lens can offer advantages for dimensional metrology. For example, these lenses can be integrated into our Multi-Sensor Video Measurement Machines.

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Figure 5: An image of two identical 8-32 cap screws imaged with our previous generation MVTC23013 0.128X Telecentric Lens. Although the screws appear to be the same size and in the same object plane, they are actually separated by a distance of approximately 45 mm along the optical axis.

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Figure 6: The same two screws photographed with our previous-generation MVL7000 conventional zoom lens. The MVL7002 lens provides similar performance. In this image, the perspective error due to the separation of the screws would lead to incorrect height measurements.

When viewing an image with a camera, the system magnification is the product of the objective and camera tube magnifications. When viewing an image with trinoculars, the system magnification is the product of the objective and eyepiece magnifications.

Magnification and Sample Area Calculations

Magnification

The magnification of a system is the multiplicative product of the magnification of each optical element in the system. Optical elements that produce magnification include objectives, camera tubes, and trinocular eyepieces, as shown in the drawing to the right. It is important to note that the magnification quoted in these products' specifications is usually only valid when all optical elements are made by the same manufacturer. If this is not the case, then the magnification of the system can still be calculated, but an effective objective magnification should be calculated first, as described below.

To adapt the examples shown here to your own microscope, please use our Magnification and FOV Calculator, which is available for download by clicking on the red button above. Note the calculator is an Excel spreadsheet that uses macros. In order to use the calculator, macros must be enabled. To enable macros, click the "Enable Content" button in the yellow message bar upon opening the file.

Example 1: Camera Magnification
When imaging a sample with a camera, the image is magnified by the objective and the camera tube. If using a 20X Nikon objective and a 0.75X Nikon camera tube, then the image at the camera has 20X × 0.75X = 15X magnification.

Example 2: Trinocular Magnification
When imaging a sample through trinoculars, the image is magnified by the objective and the eyepieces in the trinoculars. If using a 20X Nikon objective and Nikon trinoculars with 10X eyepieces, then the image at the eyepieces has 20X × 10X = 200X magnification. Note that the image at the eyepieces does not pass through the camera tube, as shown by the drawing to the right.

Using an Objective with a Microscope from a Different Manufacturer

Magnification is not a fundamental value: it is a derived value, calculated by assuming a specific tube lens focal length. Each microscope manufacturer has adopted a different focal length for their tube lens, as shown by the table to the right. Hence, when combining optical elements from different manufacturers, it is necessary to calculate an effective magnification for the objective, which is then used to calculate the magnification of the system.

The effective magnification of an objective is given by Equation 1:

(Eq. 1)

Here, the Design Magnification is the magnification printed on the objective, f_{Tube Lens in Microscope} is the focal length of the tube lens in the microscope you are using, and f_{Design Tube Lens of Objective} is the tube lens focal length that the objective manufacturer used to calculate the Design Magnification. These focal lengths are given by the table to the right.

Note that Leica, Mitutoyo, Nikon, and Thorlabs use the same tube lens focal length; if combining elements from any of these manufacturers, no conversion is needed. Once the effective objective magnification is calculated, the magnification of the system can be calculated as before.

Example 3: Trinocular Magnification (Different Manufacturers)
When imaging a sample through trinoculars, the image is magnified by the objective and the eyepieces in the trinoculars. This example will use a 20X Olympus objective and Nikon trinoculars with 10X eyepieces.

Following Equation 1 and the table to the right, we calculate the effective magnification of an Olympus objective in a Nikon microscope:

The effective magnification of the Olympus objective is 22.2X and the trinoculars have 10X eyepieces, so the image at the eyepieces has 22.2X × 10X = 222X magnification.

Sample Area When Imaged on a Camera

When imaging a sample with a camera, the dimensions of the sample area are determined by the dimensions of the camera sensor and the system magnification, as shown by Equation 2.

(Eq. 2)

The camera sensor dimensions can be obtained from the manufacturer, while the system magnification is the multiplicative product of the objective magnification and the camera tube magnification (see Example 1). If needed, the objective magnification can be adjusted as shown in Example 3.

As the magnification increases, the resolution improves, but the field of view also decreases. The dependence of the field of view on magnification is shown in the schematic to the right.

Example 4: Sample Area
The dimensions of the camera sensor in Thorlabs' previous-generation 1501M-USB Scientific Camera are 8.98 mm × 6.71 mm. If this camera is used with the Nikon objective and trinoculars from Example 1, which have a system magnification of 15X, then the image area is:

Sample Area Examples

The images of a mouse kidney below were all acquired using the same objective and the same camera. However, the camera tubes used were different. Read from left to right, they demonstrate that decreasing the camera tube magnification enlarges the field of view at the expense of the size of the details in the image.

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Acquired with 1X Camera Tube (Item # WFA4100)

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Acquired with 0.75X Camera Tube (Item # WFA4101)

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Acquired with 0.5X Camera Tube (Item # WFA4102)

Resolution Tutorial

An important parameter in many imaging applications is the resolution of the objective. This tutorial describes the different conventions used to define an objective's resolution. Thorlabs provides the theoretical Rayleigh resolution for all of the imaging objectives offered on our site; the other conventions are presented for informational purposes.

Resolution

The resolution of an objective refers to its ability to distinguish closely-spaced features of an object. This is often theoretically quantified by considering an object that consists of two point sources and asking at what minimum separation can these two point sources be resolved. When a point source is imaged, rather than appearing as a singular bright point, it will appear as a broadened intensity profile due to the effects of diffraction. This profile, known as an Airy disk, consists of an intense central peak with surrounding rings of much lesser intensity. The image produced by two point sources in proximity to one another will therefore consist of two overlapping Airy disk profiles, and the resolution of the objective is therefore determined by the minimum spacing at which the two profiles can be uniquely identified. There is no fundamental criterion for establishing what exactly it means for the two profiles to be resolved and, as such, there are a few criteria that are observed in practice. In microscopic imaging applications, the two most commonly used criteria are the Rayleigh and Abbe criteria. A third criterion, more common in astronomical applications, is the Sparrow criterion.

Rayleigh Criterion

The Rayleigh criterion states that two overlapping Airy disk profiles are resolved when the first intensity minimum of one profile coincides with the intensity maximum of the other profile [1]. It can be shown that the first intensity minimum occurs at a radius of 1.22λf/D from the central maximum, where λ is the wavelength of the light, f is the focal length of the objective, and D is the entrance pupil diameter. Thus, in terms of the numerical aperture (NA = 0.5*D/f), the Rayleigh resolution is:

r_R = 0.61λ/NA

An idealized image of two Airy disks separated by a distance equal to the Rayleigh resolution is shown in the figure to the left below; the illumination source has been assumed to be incoherent. A corresponding horizontal line cut across the intensity maxima is plotted to the right. The vertical dashed lines in the intensity profile show that the maximum of each individual Airy disk overlaps with the neighboring minimum. Between the two maxima, there is a local minimum which appears in the image as a gray region between the two white peaks.

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Left: Two point sources are considered resolved when separated by the Rayleigh resolution. The gray region between the two white peaks is clearly visible.
Above: The vertical dashed lines show how the maximum of each intensity profile overlaps with the first minimum of the other.

Thorlabs provides the theoretical Rayleigh resolution for all of the imaging objectives offered on our site in their individual product presentations.

Abbe Criterion

The Abbe theory describes image formation as a double process of diffraction [2]. Within this framework, if two features separated by a distance d are to be resolved, at a minimum both the zeroth and first orders of diffraction must be able to pass through the objective's aperture. Since the first order of diffraction appears at the angle: sin(θ₁) = λ/d, the minimum object separation, or equivalently the resolution of the objective, is given by d = λ/n*sin(α), where α is the angular semi-aperture of the objective and a factor of n has been inserted to account for the refractive index of the imaging medium. This result overestimates the actual limit by a factor of 2 because both first orders of diffraction are assumed to be accepted by the objective, when in fact only one of the first orders must pass through along with the zeroth order. Dividing the above result by a factor of 2 and using the definition of the numerical aperture (NA = n*sin(α)) gives the famous Abbe resolution limit:

r_A = 0.5λ/NA

In the image below, two Airy disks are shown separated by the Abbe resolution limit. Compared to the Rayleigh limit, the decrease in intensity at the origin is much harder to discern. The horizontal line cut to the right shows that the intensity decreases by only ≈2%.

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Left: Two point sources separated by the Abbe resolution limit. Though observable, the contrast between the maxima and central minimum is much weaker compared to the Rayleigh limit.
Above: The line cut shows the small intensity dip between the two maxima.

Sparrow Criterion

For point source separations corresponding to the Rayleigh and Abbe resolution criteria, the combined intensity profile has a local minimum located at the origin between the two maxima. In a sense, this feature is what allows the two point sources to be resolved. That is to say, if the sources' separation is further decreased beyond the Abbe resolution limit, the two individual maxima will merge into one central maximum and resolving the two individual contributions will no longer be possible. The Sparrow criterion posits that the resolution limit is reached when the crossover from a central minimum to a central maximum occurs.

At the Sparrow resolution limit, the center of the combined intensity profile is flat, which implies that the derivative with respect to position is zero at the origin. However, this first derivative at the origin is always zero, given that it is either a local minimum or maximum of the combined intensity profile (strictly speaking, this is only the case if the sources have equal intensities). Consider then, that because the Sparrow resolution limit occurs when the origin's intensity changes from a local minimum to a maximum, that the second derivative must be changing sign from positive to negative. The Sparrow criterion is thus a condition that is imposed upon the second derivative, namely that the resolution limit occurs when the second derivative is zero [3]. Applying this condition to the combined intensity profile of two Airy disks leads to the Sparrow resolution:

r_S = 0.47λ/NA

The image to the left below shows two Airy disks separated by the Sparrow resolution limit. As described above, the intensity is constant in the region between the two peaks and there is no intensity dip at the origin. In the line cut to the right, the constant intensity near the origin is confirmed.

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Left: Two Airy disk profiles separated by the Sparrow resolution limit. Note that, unlike the Rayleigh or Abbe limits, there is no decrease in intensity at the origin.
Above: At the Sparrow resolution limit, the combined intensity is a constant near the origin. The scale here has been normalized to 1.

References
[1] Eugene Hecht, "Optics," 4th Ed., Addison-Wesley (2002)
[2] S.G. Lipson, H. Lipson, and D.S. Tannhauser, "Optical Physics," 3rd Ed., Cambridge University Press (1995)
[3] C.M. Sparrow, "On Spectroscopic Resolving Power," Astrophys. J. 44, 76-87 (1916)