Geometric Optics | Serial

As electromagnetic waves, the properties of light can be described by many physical quantities, such as the amplitude, frequency, phase, and propagation constant of the electric field. The unit of the electric field amplitude is in volts/meter, which indicates the strength of the light field, but the physical quantity is difficult to measure directly, so people usually use the intensity to describe the intensity of a beam of light, and the magnitude of the light intensity is proportional to the amplitude of the electric field squared. The light intensity can be obtained by calculating the optical power (Power) per unit area, and the optical power can be easily measured with a power meter.

When an electromagnetic wave of a certain frequency is transmitted in space, its electric field is a function of both time and space. If we observe the distribution of the electric field in space at a specific time, we can introduce the concept of Wavelength. The reciprocal of the wavelength is called the Wavenumber, this concept is commonly used by scholars engaged in spectroscopy. Similarly, when we observe the change of the electric field with time at a specific position in space, the concept of a period can be introduced. The reciprocal of the period is the frequency of the electromagnetic wave. For visible light, the frequency of light determines the color of the light. The wavelength of a light wave is equal to the distance that light travels within a period of time. Note that when light is transmitted in different media, the period (or frequency, color) of the light remains the same, but the transmission speed of light will change depending on the medium, so the wavelength of light will also change.

Electromagnetic waves cover a very wide spectrum range, and what we often say about visible light corresponding to only a small portion of the electromagnetic wave spectrum with a wavelength of 380 nm to 780 nm. The more commonly used light sources in biological imaging are concentrated in the visible light band and the near-infrared band (380-1700 nm) with a slightly longer wavelength than visible light. The illumination sources of traditional microscopes mostly rely on mercury lamps, xenon lamps, or iodine lamps that use the principle of gas discharge. With the rapid advancement of laser technology, these traditional light sources are gradually being replaced by laser light sources.

The absorption of light by different media is also closely related to the wavelength. It is particularly important to choose the appropriate wavelength to avoid the large absorption of light by biological tissues when imaging biological tissues in depth. On the other hand, if you want to use a laser to cut biological tissue, generally choose the mid-infrared (3-4 μm) band, so that the light is strongly absorbed by the water in the biological tissue.

As we all know, light has wave-particle duality. In other words, light sometimes shows the properties of waves, and sometimes it shows the properties of particles. Besides, light also has momentum, and when interacting with the medium, it exerts a force on the medium to achieve the transfer of momentum. This is how Optical tweezers work.

The light used in biological imaging is generally visible light and near-infrared bands, with wavelengths on the order of micrometers and submicrometer, and commonly used optical devices (such as lenses, prisms, mirrors, polarizing beam splitters, etc.) The scale far exceeds the wavelength of light. In this case, we can introduce the concept of light rays to describe the energy carried by a light wave in a certain direction. Geometric optics is to use the concept of light to study various optical phenomena produced by the interaction of light and matter. Sometimes geometric optics is also called Ray Optics. For example, the principle of light transmission along a straight line in geometric optics can be used to intuitively explain the phenomenon of small hole imaging.

In fact, we have been exposed to geometric optics while studying physics in high school, and we are familiar with the laws of reflection and refraction. We know that different media have different refractive indexes. When light travels in the media, the speed of light becomes the speed in vacuum divided by the refractive index of the media, and the corresponding wavelength of light also becomes the wavelength in vacuum divided by taking the refractive index. The refractive index of most media is greater than 1, so compared with the transmission in a vacuum, the speed of light transmission in the medium becomes slower and the wavelength becomes shorter.

When light enters from medium 1 to medium 2, because the two media have different refractive indexes, reflection and refraction will occur at the interface between the two media. If the refractive index of medium 1 is greater than the refractive index of medium 2, then when the incident angle exceeds a certain critical value, a Total internal reflection phenomenon will occur, and all light will be reflected back to medium 1 at the interface.

The reason why the optical fiber transmits light is to rely on the core layer with a high refractive index and the cladding layer with a low refractive index to completely limit the light within the core layer through total reflection, thereby achieving long-distance light transmission. In the 1960s, the Chinese scientist Gao Kun theoretically predicted that the loss of glass optical fiber could be greatly reduced and could meet the needs of long-distance communication. This work opened the prelude to optical fiber communication. Gao Kun was also known as the father of optical fiber and won the Nobel Prize in Physics in 2009.

It is also worth mentioning that the diameter of the core layer of an optical fiber is generally only a few microns or less, and the light confined in the core layer may produce a relatively large light intensity (power divided by the beam area), thus resulting in a very rich non-linear optical phenomena. One of the significant consequences is that the spectrum of the incident light will greatly widen in the fiber. This phenomenon is called Supercontinuum generation. Under certain conditions, incident near-infrared light may produce a white light spectrum that can cover the entire visible band. Because the core layer of the optical fiber is very small, this wide-spectrum light source can be regarded as a point light source, which has excellent spatial coherence, and this advantage is what the traditional biological imaging illumination light source we mentioned earlier does not have. It is foreseeable that this new light source generated based on supercontinuum will be more and more widely used in biological research.

Different media have different refractive indices, and the refractive index depends not only on the media but also on the frequency of the incident light. The phenomenon that the refractive index of light in a medium depends on the frequency of light is called the dispersion of the medium. In other words, in the same medium, dispersion causes different frequencies of light to have different refractive indices. Therefore, after the white light incident on one side of the prism is refracted twice, the light of different colors (frequency) exits in different directions on the other side of the prism. As early as 1860, Kirchhoff and himself developed the world's first spectrometer using the spectral properties of prisms.

The phenomenon of light reflection and refraction is also very common in daily life, and many natural phenomena are related to this. For example, the rainbow of seven colors hanging in the sky after rain is caused by sunlight incident on the water droplets suspended in the air, after two refractions and one total reflection.

The lens is an important optical device, and its working principle relies on the light being refracted on the front and back surfaces of the lens to achieve the convergence or divergence of the incident light. Taking a convex lens as an example, the incident parallel light is converged to the focal point of the lens, and the distance from the focal point to the lens is defined as the focal length.

An index to measure the focusing (or diverging) ability of a lens is the Numerical aperture of the lens. A convex lens has a greater bending angle for parallel rays incident on the edge of the lens, and its focusing ability is stronger. Therefore, the numerical aperture is defined as the sine of the angle of the Marginal ray multiplied by the refractive index of the medium where the light exiting the lens is located.

The principle of thin-lens imaging has long been learned in high school physics. Three special rays can be used to determine the position of the image.

A single lens will introduce various aberrations. To eliminate aberrations and obtain clear and accurate imaging, the objective lens of the microscope is a lens group composed of several convex lenses and concave lenses. Generally, the side of the objective lens will identify various parameters of the objective lens.

The main content of this lecture is geometric optics that you have already learned in high school. Geometric optics may seem rough, but the methods used by many modern optical system design software (such as Oslo, CodeV, Zmax, etc.) are based on the core concept of "optical" geometric optics. In geometric optics, a thin lens focuses parallel light to a point, which seems to mean that the lens can focus the incident light into an infinitesimally small spot. But we know that the prerequisite for the establishment of geometric optics is that the optical device we consider includes a spot size that is much larger than the wavelength. Therefore, when the spot size focused by the lens is close to the wavelength scale, geometric optics is no longer valid, and the optical nature of fluctuations will be the subject of the next lecture.