Microscope objective lenses are a crucial part of a microscope, responsible for magnifying the specimen being observed. They are used to gather light from the object being observed and focus the light rays to produce a real image. The objective lens is one of the most important parts of a microscope, as it determines the microscope’s basic performance and function [3].

Gaussianbeam profile

The microscope objective will show the manufacturer (not shown in the figure), followed by the type of aberration correction; in our image, we have a “Plan Achromat” which produces a flat surface at the image plane and achromat for the type of chromatic aberration.

ABCD matrixGaussianbeam

In the previous calculation, I assumed an angle of acceptance of 72-degrees with a reasonable upper limit when working with air (that angle gives us a NA of 0.95). However, by immersing the sample and microscope in oil or another liquid, it is possible to have a larger NA. This affects not only the resolution of our image but also its brightness (the brightness is calculated as the square of its NA).

The latter are in particular very interesting, as laser light with a Laguerre-Gaussian amplitude distribution happens to have a well-defined orbital angular momentum, as first observed by L. Allen in 1992. Quoting from Allen's paper: The transverse amplitude distribution of laser light is usually described in terms of a product of Hermite polynomials $H_n(x)H_m(y)$ and associated with TEM$_{nmq}$ modes. Laguerre polynomial distributions of amplitude, TEM$_{plq}$ modes, are also possible but occur less often in actual lasers.

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Recall that a laser is an oscillator composed by an amplifier, the active medium, and a resonator, the optical cavity. The light emitted by the laser is a combination of the cavity modes, which combination depends on the cavity properties and the gain profile of the laser.

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Gaussianbeam calculator

While most lasers generate Gaussian beams, for reasons well outlined by Massimo Ortolano in his answer, this is not the only possibility. Other two kinds of laser profiles that have applications in optical laboratories are for example Hermite-Gaussian and Laguerre-Gaussian beams.

Gaussianbeam pdf

The simplest designs are usually called ‘achromat objectives’ and contain only a front lens and a couple of achromatic doublets to correct for aberrations. On the other hand, we have Apochromat microscope objectives in which several apochromatic doublets are used, in addition to some achromats for a better image quality. For a better explanation of the difference between achromatic and apochromatic lenses, please read the linked articles.

Hence, a so-called single-mode laser working on the fundamental mode of a cavity with two spherical mirrors, will have an intensity profile quite close to that of a Gaussian.

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Another specification can be “Plan Fluor” for fluorite and “APO” for apochromatic. Next we have the magnification, numerical aperture, and the immersion medium. As mentioned before, dry objective lenses usually have a NA no larger than 0.95, but that number can be considerably higher in immerse objectives. We next have an infinity symbol, meaning that the lens is infinity corrected.

Gaussianbeam intensity formula

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Even when the laser itself can only generate a fundamental Gaussian profile, the spatial profile of the light is (relatively) easily modified, for example with SLMs, and made into any profile one wants.

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Gaussian laserbefore and after

In previous entries, we have talked about the design of scanning microscopes, infinity corrected microscopes, confocal microscope design, and Koehler illumination systems-a common illumination system in microscopes. The most essential microscope element in a borescope design is the objective lens.

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In general, not all lasers are single mode and not all lasers are equipped with those kind of cavities (e.g., solid-state lasers). Therefore, not all laser beams are perfectly Gaussian. However, designers always try to choose cavity shapes which minimize the field at the edges of the cavity to reduce diffraction losses.

In cases where the objective is not meant to be used in infinity corrected microscopes, there will be a number, usually 160) referring to the length of the microscope tube. Some microscope objectives will show the letters “DIN” which stands for “Deutsche Industrial Normen.” that sets a length of 160 mm.

Objective lenses for microscopes typically have several components, including the front lens, the rear lens, the aperture, the lens barrel, and the thread. Each component plays an important role in determining the objective’s performance. For example, the aperture determines the resolution and depth of field of the objective lens, while the thread allows the objective to be attached to the microscope.

Objective lenses can have just a couple of lens elements, (an achromat and simple lens, for example) or multiple groups of elements. Even two microscope objectives with the same magnification can have a completely different design, as shown in Figure 1.

Gaussianbeam equation

Where R is the resolution, ? is the light wavelength, n is the refractive index, and θ is the half angle of the acceptance light cone (NA is the numerical angle defined as sin(θ)). For example, a microscope objective that works with visible light, with air surrounding the sample, and an acceptance half-angle cone of 72-degrees, will have a minimum resolution of 256 nm. If we surround the sample in a liquid with a refractive index of 1.5, our resolution will improve to 171 nm.

Most off the shelf microscope objectives have several body markings to better identify them. Typical markings can be seen in Figure 2.

There are three design variables that can help us calculate the microscope objective resolution: the system wavelength, the light cone captured by the objective (also known as numerical aperture), and the refractive index between the first lens of the objective and the sample. This can be expressed by the following formula:

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Gaussianbeam waist

The intensity profile is thus determined by this combination of modes. If you consider for example an optical cavity composed of two spherical mirrors, it turns out that its modes are Gaussian beams: the fundamental mode has an intensity profile which is a simple Gaussian curve, while higher modes have more complicated profiles (see e.g. this document).

The magnification of the objective lens can vary, depending on the intended use of the microscope. For example, objective lenses for biological applications typically range from 4x to 100x, while those used for metallurgical applications can range up to 200x or more [1].

In conclusion, microscope objective lenses are an essential part of a microscope and are used to magnify the specimen being observed. They consist of several components that work together to produce a clear image, and their magnification can vary depending on the intended use of the microscope.

With over 15 years of experience and 500+ unique optical systems designed, Optics for Hire specializes in advanced optical engineering. If it uses light, we've worked on it.