How Lenses, Mirrors, and Filters Work In Your Flow ...

Written by Tim Bushnell, PhD

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This article investigates the lenses, mirrors, and filters in your flow cytometer.

1. Lenses.

As the lasers interact with particles and cells at the observation point or the interrogation point, scattered and fluorescence light is generated. In order to measure this light, the cytometer needs to collect as much of it as possible. This is the job of lenses.

Howard Shapiro phrases this duty nicely when he says &#;The lenses provide spatial resolution, enabling us to collect a great deal of light coming from a very small region of space (i.e. the interrogation point) and relatively little of the light coming from other regions a very small distance away.&#;

In other words, good lenses allow us to collect the light we&#;re interested in (scattered and fluorescence light) while avoiding irrelevant light (e.g. errant laser light).

The optical collection system of a cytometer must accomplish two goals. First, it must gather as much light as possible from the interrogation point. Second, it must collimate that light so that all rays propagate parallel to each other and can travel through the collection path without diverging. The lenses on a cytometer are designed to do these two things and do them well.

The collection lens system, which usually consist of multiple lenses, is placed directly in front of the interrogation point. Collimating lenses may be positioned some distance away from the collection lens, depending on the optical design of the cytometer.

The collection lens dedicated to the detection of both fluorescence and side scatter signal is typically positioned 90° relative to the angle at which the laser beam interacts with the stream.

Forward scatter signal, on the other hand, is collected at 180° relative to the angle that the laser hits the stream (the FSC path is in front of the laser, looking at it straight-on).

Figure 4 below illustrates a generalized configuration of the optics at the interrogation point, as seen from above, looking down at the cytometer.

One prominent feature of the forward scatter detection system is the obscuration bar. This device prevents laser light from hitting the forward scatter detector. Because of its position, the forward scatter collection paths &#;look&#; directly at the laser beam. If there wasn&#;t any device that blocked non-scattered laser light, any relevant forward scatter signal that found its way to the FSC detector would be entirely drowned out by laser light.

The obscuration bar is a horizontal piece of metal that blocks laser light but allows scattered light to pass over it and into the detector.

Figure 5 below shows how the forward scatter obscuration bar interacts with laser light.

Many cytometers use optical fibers to direct collected light to the fluorescence and side scatter detection system. In these types of systems, the output of the collection lens is focused on the ends of fibers, which are routed to the detection path. This can be very advantageous in overall cytometer design.

Detection paths can be integrated in spaces in the instrument that they would not be able to otherwise thanks to the flexible path that fibers offer.

In some systems, the lens and the fibers are directly coupled using optical gel which may minimize light loss due to refraction.

As light passes through different types of mediums (water, quartz, and air), it bends at the media interfaces. The degree to which this occurs depends on the difference in refractive index between the two mediums: the greater the difference, the more refraction occurs. By coupling the lens, which is typically glass or quartz, to material with a similar refractive index, like gel, there may be less loss as light transitions between the mediums.

The downside of gels is that they can crack and uncouple the lens from the fibers, which will prevent most collected light from entering the fibers and require a service engineer to repair.

Some cytometers use optical fibers to deliver lasers to the interrogation point. This strategy also provides a space-saving benefit in terms of where the lasers can be positions in the instrument. However, a downside to this approach is that there can be significant power loss between the laser output and the interrogation point as laser light travels through the fiber.

Additionally, fibers are not compatible with higher energy light, especially UV wavelengths, which can degrade the material of the fiber over time and require frequent replacement.

2. Mirrors.

Once light has been collected and collimated from the interrogation point, it must be partitioned by wavelength so that each detector can be dedicated to the measurement of a specific spectral band.

Again, Shapiro phrases this very elegantly: &#;Optical filters (and mirrors) provide spectral resolution, allowing discrimination between scattered, fluorescent, and background light.&#;

Mirrors generally direct and partition light through the detection path while filters are placed directly in front of each detector to ultimately determine the band or wavelength range of light that interacts with that detector.

Dichroic mirrors are pieces of glass that are coated on one side with a material that allows light above or below a certain wavelength to pass through while reflecting the rest. Placed at 45° relative to the direction of incident or oncoming light, dichroic mirrors come in longpass and shortpass flavors. A 600 LP (longpass) mirror, for example, reflects light shorter than 600 nm while allowing light longer than 600 nm to pass through. A 600 SP (shortpass) would do the opposite.

The activity of a dichroic mirror is best illustrated using a graph of percent transmission (how much gets through) as a function of wavelength.

Figure 6 below is a transmission graph from the product information of a 590 LP mirror manufactured by Chroma Technologies, one of the primary manufacturers of optical filters and mirrors used in flow cytometry.

https://www.chroma.com/products/parts/t590lpxr#tabs-0-main-2

At wavelengths below 600 nm, the transmission of light drops off precipitously using this 590 LP mirror. At 590 nm, transmission is 50% and continues to drop quickly. All of the non-transmitted light is reflected.

Dichroic mirrors are positioned in the optical detection path so that the coated surface faces the incident beam of light. You may be wondering what the effect would be if the mirror were installed backwards, so that the uncoated side were facing the direction of oncoming light. Interestingly, it probably wouldn&#;t have much effect at all.

The light that passes through the mirror would not be affected. However, the reflected light may bend slightly by the time it is reflected. If the filter is installed &#;backwards&#;, the incident light would travel through glass twice &#; once to reach the coating and once after it is reflected from the coating &#;which may result in some refraction.

In practice, this usually has little impact on fluorescence measurements. Certainly, installing dichroics backwards isn&#;t recommended but it is interesting that the effect of doing so is not as severe as it may seem.

3. Filters.

Filters are pieces of glass coated on both sides that allow light of a certain collection, or band, of wavelengths to pass through while absorbing or interfering with photons of other wavelengths.

These come in bandpass, longpass, and shortpass flavors. Bandpass filters are the ones that are most commonly used in flow cytometry. Positioned in front of the detectors, these components determine what collection of wavelengths, and ultimately which fluorophores, will be measured by each detector. Bandpass filters are named based on the center and width of the band of light that will pass through.

For example, a 525/50 filter allows light to pass that is of a range of wavelengths of 500-550 nm (525 +/- 50 nm). Note that the entire band&#;s width is 50 nm &#; the range is not 525+/-50 nm but is 525+/-25 nm (25 nm on either side of the center wavelength).

Figure 7 below illustrates the transmission curve, from Chroma Technologies, of a 525/50 bandpass filter.

https://www.chroma.com/products/parts/et525-50m

As shown, the transmission of this filter drops almost asymptotically at 500 nm and at 550 nm. This particular filter, given its transmission band, is ideal for measuring fluorescence of FITC, GFP, or any other fluorophore with similar emission spectra.

Finally, Figure 8 integrates both dichroic mirrors and bandpass filters to illustrate how they cooperate in a detection path. The arrows represent the direction of light as it passes through the path.

One final comment about filters. While they are, for the most part, very good at letting relevant light pass and keeping out irrelevant light, there are certain circumstances when the wrong kind of light &#; especially laser light &#; can sneak past the guards and sabotage detection.

This is most typically a problem in the &#;PE&#; channel measured off the 561 nm laser.

This channel&#;s bandpass&#; center is usually centered around 575-590 nm and its longer (wavelength) edge can be precariously close to 561 nm. There is some variability in filters as well, that result in laser light leakage.

Finally, filters are only able to block up to a certain point. If enough light &#; say, high-powered laser light &#; is directed on them, a certain proportion of that light will pass through. The effect of all these extraneous photons can be severe.

Excessive background light in a detector can cause a drastic loss in sensitivity. If measuring 8-peak beads under conditions of high optical background, you will see both the dim peaks much higher on the scale than they would be otherwise, as well as merging of peaks.

Knowing this can be useful for troubleshooting. If you are having trouble resolving a population in a channel, especially one close to a laser line, it may be worth investigating a laser light leakage issue into that channel. 8-peak beads can be a useful first-line diagnostic tool in this regard.

This article outlined some of the major components of the optical systems used in flow cytometry. While it is certainly possible to explore these topics in much more depth, what is presented here should provide enough insight to understand what happens before a signal is produced from the PMT detectors. Additionally, this article may also equip you with a knowledge toolkit that can help troubleshoot problems you may encounter when performing your next cytometry experiment.

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A mirror is an optical device which can reflect light. Usually, only those devices are meant where the reflection is of specular type and the angle of reflection equals the angle of incidence (see Figure 1). This means that reflective diffusers and diffraction gratings, for example, are not considered as mirrors, although they can also reflect light.

A somewhat more general term is reflector. While all mirrors are reflectors, there are reflectors which are somewhat more complex than a simple mirror, e.g. prisms used as retroreflectors, using more than one total internal reflection at a prism surface.

Mirror surfaces are not necessarily flat; there are mirrors with a curved (convex or concave) reflecting surface (see below).

This article deals mostly with optical mirrors as used in optics and laser technology, for example, and in other areas of photonics.

Properties of a Mirror

Various basic properties characterize a mirror:

Figure 1:

Reflection of light on a mirror.

• The reflectivity (or reflectance) is the percentage of the optical power which is reflected. Generally, it depends on the wavelength and the angle of incidence, for non-normal incidence often also on the polarization direction.
• The reflection phase is the phase shift of reflected light, i.e., the optical phase change obtained when comparing light directly before and directly after the reflection. The phase shift can depend on the wavelength and the polarization direction. If the phase change is different between s and p polarization (for non-normal incidence), the polarization state of incident light will in general be modified, except if it is purely s or p polarization. That is exploited in phase-retarding mirrors, e.g. for converting linearly polarized light into circularly polarized light.
• Mirrors work only in a limited wavelength range, i.e., they exhibit the wanted reflectivity only within that range. The width of that range is called the reflection bandwidth. Of course, its exact value generally depends on the angle of incidence, the polarization and on the tolerance for the reflectivity.
• Similarly, there can be a limited range of angles of incidence, particularly for dielectric mirrors.
• The surface shape (e.g. spherically convex curved) is also relevant, see below.

Additional properties can be relevant in various applications:

• A high surface quality is often important in laser technology. The surface flatness of laser mirrors and others is often specified in wavelengths, e.g. λ / 10. As surface defects are largely a random phenomenon, only worst-case or statistical specifications can be given. For small localized defects, it is common to give &#;scratch & dig&#; specifications according to the US standard MIL-REF-B: there are two numbers, quantifying the severity of scratches (shallow markings or tearings) and digs (pit-like holes) basically by a comparison of their visual appearance with those of defects in certain standard parts. A quality figure of simple parts could be 80-50, a commercial quality is 60-40, laser mirrors should normally have 20-10 or better, and high precision parts can have 10-5. There is also the standard ISO -7, which also contains a more rigorous definition based on the size of defects rather than only their visual appearance.
• For use with high-power lasers, the optical damage threshold may be of interest &#; particularly in conjunction with pulsed lasers, as these tend to have high peak powers. It is often specified for nanosecond pulses.

Types of Mirrors

Metal-coated Mirrors &#; Back Side and First Surface Mirrors

Ordinary mirrors as used in households are often silver mirrors on glass. These basically consist of a glass plate with a silver coating on the back side. The coating is thick enough to suppress any significant transmission from any side. Nevertheless, the reflectivity is substantially below 100%, since there are absorption losses of a few percent (for visible light) in the silver layer.

Household mirrors typically have the coating on the back side, so that one has a robust glass surface outside, which can be cleaned easily, and the coating on the back side (with an additional layer) is well protected. For other applications, one uses first surface mirrors, where the light is incident directly on the coating and does not reach the mirror substrate.

For use in laser technology and general optics, more advanced types of metal-coated mirrors have been developed. These often have additional dielectric layers on top of the metallic coating in order to improve the reflectivity and/or to protect the metallic coating against oxidation (enhanced and protected mirrors). Different metals can be used, e.g. gold, silver, aluminum, copper, beryllium and nickel/chrome alloys. Silver and aluminum mirrors are particularly popular. Others are mostly used as infrared mirrors.

The article on metal-coated mirrors gives more details.

Dielectric Mirrors

The most important type of mirror in laser technology and general optics is the dielectric mirror. This kind of mirror contains multiple thin dielectric layers. One exploits the combined effect of reflections at the interfaces between the different layers. A frequently used design is that of a Bragg mirror (quarter-wave mirror), which is the simplest design and leads to the highest reflectivity at a particular wavelength (the Bragg wavelength).

In contrast to some metal-coated mirrors, dielectric mirrors are usually made as first surface mirrors, which means that the reflecting surface is at the front surface, so that the light does not propagate through some transparent substrate before being reflected. That way, not only possible propagation losses in the transparent medium are avoided, but most importantly additional reflections at the front surface, which could be particularly relevant for non-normal incidence.

Generally, dielectric mirrors have a limited reflection bandwidth. However, there are specially optimized broadband dielectric mirrors, where the reflection bandwidth can be hundreds of nanometers. Some of those are used in ultrafast laser and amplifier systems; they are sometimes called ultrafast mirrors, and they also need to be optimized in terms of chromatic dispersion.

Laser mirrors as used to form laser resonators, for example, are also usually dielectric mirrors, having a particularly high optical quality and often a high optical damage threshold. Some of them are used as laser line optics, i.e., only with certain laser lines. Also, there are supermirrors with a reflectivity extremely close to 100%, and dispersive mirrors with a systematically varied thin-film thickness. They can be used for high-Q optical resonators, for example.

In some cases, dielectric mirrors should also be polished on the back side &#; in particular, when some amount of light transmission is required, e.g. for output couplers of lasers.

Dielectric mirrors can be designed as cold mirrors or hot mirrors, which both can be used for removing unwanted infrared radiation &#; usually for reducing the thermal load on an optical system.

See the article on dielectric mirrors for more details.

Dichroic Mirrors

Dichroic mirrors are mirrors which have substantially different reflection properties for two different wavelengths. They are usually dielectric mirrors with a suitable thin-film design. For example, they can be used as harmonic separators in setups for nonlinear frequency conversion.

Curved Mirrors

While many mirrors have a plain reflecting surface, many others are available with a curved (convex or concave) surface, for example for focusing laser beams or for imaging applications.

Most curved mirrors have a spherical surface, characterized by some radius of curvature <$R$>. A mirror with a concave (inwards-curved) surface acts a focusing mirror, while a convex surface leads to defocusing behavior. Apart from the change of beam direction, such a mirror acts like a lens. For normal incidence, the focal length (disregarding its sign) is simply <$R / 2$>, i.e., half the curvature radius. For non-normal incidence with an angle <$\theta$> against the normal direction, the focal length is <$(R / 2) \cdot \cos \theta$> in the tangential plane and <$(R / 2) / \cos \theta$> in the sagittal plane.

There are also parabolic mirrors, having a surface with a parabolic shape. For tight focusing, one often uses off-axis parabolic mirrors, which allow one to have the focus well outside the incoming beam.

Deformable Mirrors

There are deformable mirrors, where the surface shape can be controlled, often with many degrees of freedom (possibly several thousands). Such mirrors are mostly used in adaptive optics for correcting wavefront distortions.

Variable Reflectivity Mirrors

While most mirrors have a uniform reflectance across their reflecting area, there are also variable reflectivity mirrors, where the reflectance depends on the position. These are also called graded reflectivity mirrors. They are used in lasers with unstable resonators, also as variable optical attenuators.

Mirrors for Special Functions

Some types of mirrors are used for special functions:

Phase-retarding Mirrors

Phase-retarding mirrors are made such that they introduce a well defined phase difference for s- and p-polarized components of a beam. For example, they can be used for converting linearly polarized light into circularly polarized light if that phase difference is <$\pi /2$>.

Absorbing Thin-film Reflectors

Absorbing thin-film reflectors are metal-coated mirrors which are designed to reflect e.g. s-polarized light at 45° angle of incidence while absorbing p-polarized light with the same direction of incidence. They work e.g. at the common CO2 laser wavelength of 10.6 μm and can be used in conjunction with a phase-retarding mirror to build a kind of polarization-based optical isolator. Such a device can e.g. be used for preventing light reflected on a workpiece from getting back to the laser. However, it can be used only for moderate power levels because otherwise the absorbed power would destroy the mirror or at least degrade its performance.

Substrate Shapes

Mirror substrates in optics and laser technology often have a cylindrical form, for example with a diameter of 1 inch and a thickness of a couple of millimeters. However, there are also substrates with a rectangular, elliptical or D-shaped front surface, for example. Besides, there are prism mirrors, where a reflecting coating is placed on a prism, and retroreflectors.

For special applications, a mirror substrate with a tiny hole is used. This can be useful, for example, for combining two laser beams, one of which is sent in a focused fashion through the hole while the other beam, having a substantially larger diameter, is reflected on the mirror surface.

Mirrors in Fiber Optics

In fiber optics, it is also often required to reflect light &#; in most cases back into the fiber where the light came from. That can be achieved simply by butting a normal kind of mirror (e.g. a dielectric mirror] to a normally cleaved fiber end. Alternatively, one may apply a dielectric coating directly on a fiber end.

There are also completely different types of fiber reflectors, e.g. fiber loop mirrors which are strictly speaking no mirrors but another type of reflectors.

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