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To simplify this further, as light travels through one medium to another, it changes speed (e.g. when passing from air to water, light slows down). When light passes across the boundary of two different medium at an angle other than 900, this results in a change of direction. Although the frequency of light doesn’t change, the resultant wavelength will be determined by nature of the medium.

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There is an inverse relationship between the angular aperture and the working distance of an objective. I have covered working distance in my article entitled ‘Looking Down and Through: Microscope Optics 3: Oil Immersion Objectives’, but to briefly recap, the working distance is the actual distance (in millimetres or microns) between the objective front lens and the surface of the cover slip when the object is in sharp focus. Objectives with short working distances will consequently have a greater ability to gather more oblique light rays from a specimen compared to longer working distance objectives. Angular aperture is usually determined by the optics within the objective and each objective lens will have an optimal focal length and working distance- it can’t simply be increased by moving the objective closer to the slide!

Polarization Dependent Loss (PDL) can be defined as the maximum change observed in transmittance or reflectance at a given wavelength as the light is cycled through all possible polarization states. The PDL can be calculated based on the difference between the s- and p-polarization states of light, i.e.,

Highpass filter

This is a region of high reflectance. It is specified by a reflect-band width in nm at a certain transmittance level relative to the peak transmittance, e.g.,

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Numerical aperture is proportional to refractive index. For example, air has a refractive index of 1.00, water has a refractive index of 1.33, whereas many of the immersion oils have refractive indexes around 1.52.

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This is the average or mean wavelength based on two points on the curve at the same transmittance level. A typical level is at Full Width Half Maximum (FWHM) or -3dB. At this level any ripple or other pass-band defect will not effect the center wavelength calculation.

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Second orderfilter

This is a region of high transmittance. It is usually specified by a pass-band width, peak IL and ripple. The pass-band width is specified in nm at a certain transmittance level relative to the peak transmittance.

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This magnification calculator calculates magnification instantly with the help of the lens focal length and the distance of the object being provided.

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Therefore, the refractive index of air is a limiting factor in achieving the highest possible NA of an objective. As a result, objectives with NA values greater than one are the immersion objectives where the air gap is replaced by a medium such as water or oil. An angular aperture of 1800 is physically unachievable- the widest angle of light which can be collected by an objective is around 1440. Consequently, the maximum achievable NA of a non-immersion objective is approximately 0.95 (which is equal to the sine of 72).

This is the region between a pass-band and a reflect band. This regions is called a dead-band or roll-off region and it does not typically contain any transmittance specifications. The roll-off slope is usually inherent in the pass-band and the reflect-band specifications.

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Where ‘n’ is the refractive index of the medium between the cover glass and the objective front lens (e.g. air, water or oil).

To help to understand NA, it is useful to also have some understanding of refraction. In microscopy and optics, refraction refers to the change in direction of light waves which results from a change in the medium though which light passes (for example, glass, air, oil or water).

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Bandpassfilter

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The reflect-band can also be specified by defining a center wavelength (CWL), reflect-band width and operating wavelength range, e.g.,

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The theoretical maximum angular aperture of light entering the front lens of an objective is 1800. This would give a θ value of 900 (half of the angle of the light cone). As a result, the theoretical maximum NA of an objective would be one (which is equal to the sine of 90). The refractive index of air is also one, therefore the maximum (theoretical) NA of an objective with an air gap between the front lens and the specimen would only equal one.

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The NA of an objective is the simply the ability of the lenses to collect light at a fixed distance from the sample which you are viewing. When light passes through and leaves a specimen, it enters the front lens of an objective as an inverted cone. However, a percentage of this image-forming light is refracted and reflected. Objectives which have a high NA allow for increasingly oblique light waves to be collected by the front lens which will in turn form a final image which is not only relatively brighter, but contains more information and detail and is highly resolved.

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Usually the passband ripple is specified as the difference between the maximum and minimum transmittance in the passband width (see above figure). Note that this passband ripple is different from that of a substrate etalon ripple.

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Snell’s Law describes the relationship between the angles of incidence and refraction of light as it travels through the boundary of two different medium (e.g. from air to glass). The Law states that the ratio of the sines of the angles of incident and refracted light are equivalent to the reciprocal of the ratio of the refractive indices through which the light passes.

Metaphorically, think of it this way: if you are standing in front of a door with a key hole which leads into another room, then when you are at a distance, you will only be able to see a little of the light and objects within the room. If you press your eye against the key hole, you will then see more of the detail and light in the room as you have, in theory, increased the angular aperture of your eye.

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All-passfilter

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Band Pass Filters (BPFs) are used to pass (transmit) a range of wavelengths and to block (reflect) other wavelength on either side of the bandpass. The region of high transmittance is known as the passband and the region of high reflectance is known as the reject or reflect band. The pass-band and reflect-bands are separated by the roll-off region. The complexity of these filters depends primarily on the steepness of the roll-off region, the width of the pass-band and also on the ripple and insertion loss specifications in the pass-band. In the case of a relatively high angle of incidence, polarization dependent loss may also be a consideration.

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In summary, without a correspondingly high NA, a high magnification objective will have low resolution. Most microscope companies offer objectives which have high NA values for use with immersion medium. If you are in the lucky position of buying a custom microscope, or buying new objectives for your existing instrument, you should always consider buying objectives which offer the highest NA value which you can afford.

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Lowpass filter

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Refraction is described in a formula known as ‘Snell’s Law’. Refraction was first described in the year 984 by a Persian physicist and mathematician called Ibn Sahl. In 984, he presented a manuscript in which he described how mirrors and curved lenses focused and bent light. Snell’s Law is actually named after a Dutch mathematician and astronomer called Willebrord Snellius (1580-1626). Although he was credited for mathematically describing refraction, it is more accurate to say that he ‘rediscovered’ diffraction after the work of Ibn Sahl.

Etched onto the barrel of each objective on a microscope, you will find a variety of information. In addition to the magnification and the optical correction (see my article published entitled ‘Looking Down and Looking Through: The Optics of a Microscope 2: The Objectives’ for more information on aberrations and corrections), you will find a number without units. This is the Numerical Aperture (or ‘NA’) of the objective.

This is difference between the maximum reflectance in the pass-band and the minimum reflectance in the reflect-band. The minimum reflectance in the reflect-band is very often close to 0 dB so that the reflection isolation is typically dominated by the maximum reflectance in the passband. For filters with no absorption, the transmittance and reflectance must add up to unity. Hence, there is often a relationship between the specified reflection isolation in the passband and the sum of the peak IL and ripple in the passband, i.e.,

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If the reflection isolation is specified to be -15 dB (corresponding to a reflectance of 3.2 %), then as T+R =1, the minimum transmittance in the passband is given by T=100-3.2=96.8 % which is equivalent to a 0.14 dB transmittance loss. Hence, to achieve a reflectance isolation of -15 dB, the transmittance loss must be less than 0.14 dB. Note that if a minimum allowed transmittance loss of 0.2 dB is specified along with a reflectance isolation of -15 dB, then the overriding transmittance loss to achieve the necessary reflectance isolation is 0.14 dB.

The NA of an objective is an important aspect as it relates to the final image formation seen when looking down through the eyepieces (which will be covered in full in a forthcoming blog article). Briefly, resolution relates to the amount of detail which can be seen in the final formation of an image. An objective with a high magnification would be unable to resolve detail in your sample without a similarly high NA.

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Where ‘θ’ is half of the angle of the cone of light which is collected by the front lens lens (i.e., the angular aperture).

The light from the microscope source passes through the specimen/slide and continues through the air (or an immersion medium) as a cone of light between the cover glass and the objective front lens. The ‘angular aperture’ refers to the maximum angle of the edges of this image-forming cone of light which can be collected by the objective front lens when the specimen is in focus. In addition to an increasing NA, image brightness and image detail (resolution) are also related to the angular aperture.

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