Microscope Illumination for Liquid Crystal Observation

When referencing books on biological microscopes for illumination methods suitable for liquid crystal observation, the standard illumination method presented is Köhler illumination. However, in books on polarizing microscopes used in mineralogy, the term Köhler illumination does not appear. Instead, they introduce orthoscopic illumination methods and a technique called conoscopic observation along with its associated illumination methods. Here, we will explore the relationship between these methods and discuss the most appropriate illumination techniques for liquid crystal observation.

Illumination in Biological Microscopes

In biological microscopy, "Köhler illumination" is the standard illumination method. Köhler illumination allows independent control of the illumination area and the numerical aperture (NA) of the illumination light, providing a highly uniform illumination intensity on the sample surface.

In Köhler illumination, the aperture diaphragm located at the focal plane of the light source and condenser is conjugate with the aperture plane, while the field diaphragm and sample surface form another set of conjugate planes. Since the field diaphragm and sample surface are conjugate, adjusting the field diaphragm changes the illuminated area on the sample surface. Moreover, because the aperture diaphragm is at the focal plane on the illumination side of the condenser, the NA of the illumination can be adjusted using the aperture diaphragm. As various points of light from the light source are mixed at the field diaphragm plane, there is minimal unevenness in brightness, resulting in a uniformly bright image on the sample surface.

Beyond the objective lens, the aperture diaphragm, the back focal plane of the objective lens, and the eyepoint above the eyepiece are conjugate planes. The conjugate plane of the field diaphragm includes the sample surface, the real image plane formed by the objective lens, and the retinal plane.

In addition to Köhler illumination, two other illumination methods, critical illumination and diffuse illumination, are introduced in biological microscopy texts. Critical illumination is a method where the light source and sample surface are conjugate planes, providing ample brightness and a large NA. However, since the light source and sample surface are conjugate, if a tungsten lamp is used as the light source, the filament image of the light source may overlap with the observed sample. Diffuse illumination involves positioning the condenser's focal point significantly below the sample surface, resulting in a widely spread illumination at the sample surface. This method provides high uniformity in brightness, but the illumination has a low NA and reduced light intensity. Direct irradiation using the light source without the use of condensing lenses is also a type of diffuse illumination.

In biological research, polarizing microscopes are used to visualize transparent structures, requiring high resolution; therefore, high NA Köhler illumination, similar to that used in standard bright-field observation, is necessary. As will be discussed later, the colors observed in polarized light can change depending on the NA of the illumination light. However, in biological observations, polarization is used to visualize colorless samples with small optical path differences (OPDs), so the color changes are not considered problematic.

Illumination in Mineral Microscopy

Textbooks on polarizing microscopes used in mineralogy describe two main illumination methods. One is for orthoscopic observation, where illumination with parallel light rays (NA = 0) is recommended. The other is for conoscopic observation, which requires high NA illumination comparable to that of the objective lens. However, it is unclear whether this is Köhler illumination, critical illumination, or another method, as I have not seen a detailed explanation on this matter.

For example,in Tsuboi's "Polarizing Microscope", a faouse Japanese textbook, it states that the top lens should be removed for orthoscopic observation and inserted for conoscopic observation. With the top lens removed, the NA of the illumination system is at most around 0.2, and the focal point is significantly above the stage surface. When the top lens is inserted, the NA can reach around 0.9, and the focal point is approximately 1 mm above the stage surface.

With the top lens removed, even if you adjust the position of the field diaphragm of the illumination system, it is not possible to form a field diaphragm image near the stage surface, so Köhler illumination cannot be achieved. Furthermore, even if Köhler illumination were possible, with the top lens removed, the condenser's NA would still result in low-NA illumination.

Orthoscopic observation is conducted under low-NA illumination because, in birefringent materials, the optical path length and birefringence differ between normally incident light and obliquely incident light, leading to variations in the polarization colors. Using high-NA illumination would mix different polarization colors, making it difficult to distinguish the characteristic colors of the sample.

On the other hand, conoscopic observation involves observing the polarization colors corresponding to the optical path differences (OPDs) of light passing through the sample at various angles. Therefore, the NA of the illumination light needs to be similar to that of the objective lens.
Below figures show conoscopic images (left) and orthoscopic images (right) of the same sample observed under low NA  illumination. With low NA illumination, the colors observed in the conoscopic image are almost monochromatic, and the orthoscopic image shows similar hues.

Fig. x  Conoscopic (left) and orthoscopic (right) images under low NA illumination.

In the high NA conoscopic image, colors different from the center are visible at points away from the center. Meanwhile, the orthoscopic image becomes a composite of all these colors, resulting in a nearly neutral color. If the NA of the illumination is increased to enhance resolution, the colors may change in ways that make them incomparable to standard polarization color charts.

Fig. x  Conoscopic (left) and orthoscopic (right) images under high NA illumination.

Illumination for Liquid Crystal Observation

　生物系と鉱物系の照明は上述にように根本的に異なったものです。では、液晶系の照明はどのようにすべきでしょうか。液晶の組織観察の照明で注意すべきことは、斜入射光による見え方のずれを起こさないようにすることです。 As discussed, the illumination methods for biological and mineral observations are fundamentally different. So, what should be the approach for liquid crystal observation? When illuminating liquid crystals for structural observation, it's crucial to avoid image change caused by oblique incident light.

For horizontally aligned cells of optically uniaxial rod-like nematic liquid crystals, the OPD decreases as the optical path length increases due to the reduced birefringence of oblique incident light within the plane defined by the director and the microscope's optical axis. Conversely, in planes perpendicular to the director, oblique incident light increases the OPD because the optical path length increases without a change in birefringence. The overlap of colors corresponding to increasing and decreasing OPDs broadens the spectral width, reducing color purity. However, unless the NA is significantly large, there shouldn't be a drastic change in color.

On the other hand, in cases of pronounced biaxiality, such as in the SmCA phase, the color can change significantly due to oblique incident light. Even in uniaxial cases, where the molecules are slightly tilted from perpendicular to the substrate, the situation differs greatly. Consider the scenario where the SmA phase, vertically aligned, undergoes a second-order transition to the SmC phase. As the SmC phase transition occurs, the molecular long axis tilts from the microscope's optical axis, and Schlieren textures become observable under parallel light illumination. However, if the NA of the illumination exceeds the tilt angle of the SmC phase, not only does the contrast of the Schlieren texture decrease, but the four-brush defect may also appear as a faint two-brush defect.

From this, it seems that, like mineral observations, low NA illumination is preferable for observing liquid crystal structures. But is it sufficient to remove the top lens of a swing-out condenser and use diffuse illumination? There may be cases where it is necessary to precisely limit the illumination area, in which case Köhler illumination may be preferable. Specifically, when observing thin films with low OPDs, it is necessary to limit the illumination area to prevent scattered light from regions outside the observation area from interfering with the observation.

For typical swing-out condensers, inserting the top lens allows Köhler illumination, but this reduces the working distance of the condenser to about 1 mm, making it difficult to use Köhler illumination with a hot stage. To perform Köhler illumination with a hot stage, a long-working-distance condenser compatible with the hot stage is required. For example, with Mettler's hot stage, the distance from the bottom of the hot stage to the sample contact surface is 15 mm. Considering the thickness of the slide glass, a condenser with a working distance of at least 16 mm is needed.

There are very few condensers with a working distance of 16 mm or more. However, if you are a Nikon Optiphot user, you can attach a long-working-distance condenser designed for Diaphot, which has a working distance of over 20 mm. While new ones are not available, you can find used ones at a reasonable price.
 

Conoscopic Observation and Köhler Illumination