By examining the numerical aperture equation, it is apparent that refractive index is the limiting factor in achieving numerical apertures greater than 1.0. Therefore, in order to obtain higher working numerical apertures, the refractive index of the medium between the front lens of the objective and the specimen must be increased. Microscope objectives are now available that allow imaging in alternative media such as water (refractive index = 1.33), glycerin (refractive index = 1.47), and immersion oil (refractive index = 1.51). Care should be used with these objectives to prevent unwanted artifacts that will arise when an objective is used with a different immersion medium than it was designed for. We suggest that microscopists never use objectives designed for oil immersion with either glycerin or water, although several newer objectives have recently been introduced that will work with multiple media. You should check with the manufacturer if there are any doubts.

Please note: The last two measurements do not refer directly to the size of the sensor – rather, they are derived from the size of the video camera tubes which were used in televisions

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At one point it was necessary to develop sensors with more and more pixels, as the earliest types were not sufficient for the demands of printing. That barrier was soon broken but sensors continued to be developed with a greater number of pixels, and compacts that once had two or three megapixels were soon replaced by the next generation of four of five megapixel variants. This has now escalated up to the 20MP compact cameras on the market today. As helpful as this is to manufacturers from a marketing perspective, it did little to educate consumers as to how many were necessary – and more importantly, how much was too much.

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CCD and CMOS sensors differ in terms of their construction. CCDs collect the charge at each photosite, and transfer it from the sensor through a light-shielded vertical array of pixels, before it is converted to a signal and amplified. CMOS sensors convert charge to voltage and amplify the signal at each pixel location, and so output voltage rather than charge. CMOS sensors may also typically incorporate extra transistors for other functionality, such as noise reduction.

A sensor is a solid-state device which captures the light required to form a digital image. While the process of manufacturing a sensor is well outside of the scope of this feature, what essentially happens is that wafers of silicon are used as the base for the integrated circuit, which are built up via a process known as photolithography. This is where patterns of the circuitry are repeatedly projected onto the (sensitized) wafer, before being treated so that only the pattern remains. Funnily enough, this bears many similarities to traditional photographic processes, such as those used in a darkroom when developing film and printing.

This feature of increasing numerical aperture across an increasing optical correction factor in a series of objectives of similar magnification holds true throughout the range of magnifications as shown in Table 1. Most manufacturers strive to ensure that their objectives have the highest correction and numerical aperture that is possible for each class of objective.

Figure 3(a) illustrates a hypothetical Airy disk that essentially consists of a diffraction pattern containing a central maximum (typically termed a zeroth order maximum) surrounded by concentric 1st, 2nd, 3rd, etc., order maxima of sequentially decreasing brightness that make up the intensity distribution. Two Airy disks and their intensity distributions at the limit of optical resolution are illustrated in Figure 3(b). In this part of the figure, the separation between the two disks exceeds their radii, and they are resolvable. The limit at which two Airy disks can be resolved into separate entities is often called the Rayleigh criterion. Figure 3(c) shows two Airy disks and their intensity distributions in a situation where the center-to-center distance between the zeroth order maxima is less than the width of these maxima, and the two disks are not individually resolvable by the Rayleigh criterion.

A pixel contains a light sensitive photodetector, which measures the amount of light (photons) falling onto it. This process releases electrons from the silicon, which forms the charge at each photosite.

The largest sensor size found in 35mm DSLRs. It shares its dimensions with a frame of 35mm negative film, and so applies no crop factor to lenses. It used to be the reserve of very high-end cameras, for professionals only, but the technology is getting more affordable. It also used to be true that full-frame sensors could only be found in very large cameras, but some manufacturers have found ways to shrink camera sizes while keeping a large sensor.

Every digital camera has at its heart a solid-state device which, like film, captures the light coming in through the lens to form an image. This device is called a sensor. In this article we explain the different sensor types and sizes.

A well as being an analogue device, a sensor is also colourblind. For it to sense different colours a mosaic of coloured filters is placed over the sensor, with twice as many green filters as there are of each red and blue, to match the heightened sensitivity of the human visual system towards the colour green. This system means that each pixel only receives colour information for either red, green or blue – as such, the values for the other two colours has to be guessed by a process known as demosaicing. The alternative to this system the Foveon sensor, which uses layers of silicon to absorb different wavelengths, the result being that each location receives full colour information.

Field of view microscope

Where R is resolution (the smallest resolvable distance between two objects), NA equals numerical aperture, λ equals wavelength, NA(obj) equals the objective numerical aperture, and NA(Cond) is the condenser numerical aperture. Notice that equation (1) and (2) differ by the multiplication factor, which is 0.5 for equation (1) and 0.61 for equation (2). These equations are based upon a number of factors (including a variety of theoretical calculations made by optical physicists) to account for the behavior of objectives and condensers, and should not be considered an absolute value of any one general physical law. In some instances, such as confocal and fluorescence microscopy, the resolution may actually exceed the limits placed by any one of these three equations. Other factors, such as low specimen contrast and improper illumination may serve to lower resolution and, more often than not, the real-world maximum value of R (about 0.25 µm using a mid-spectrum wavelength of 550 nanometers) and a numerical aperture of 1.35 to 1.40 are not realized in practice. Table 2 provides a list resolution (R) and numerical aperture (NA) by objective magnification and correction.

An important concept to understand in image formation is the nature of diffracted light rays intercepted by the objective. Only in cases where the higher (1st, 2nd, 3rd, etc.) orders of diffracted rays are captured, can interference work to recreate the image in the intermediate image plane of the objective. When only the zeroth order rays are captured, it is virtually impossible to reconstitute a recognizable image of the specimen. When 1st order light rays are added to the zeroth order rays, the image becomes more coherent, but it is still lacking in sufficient detail. It is only when higher order rays are recombined, that the image will represent the true architecture of the specimen. This is the basis for the necessity of large numerical apertures (and subsequent smaller Airy disks) to achieve high-resolution images with an optical microscope.

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Correct alignment of the microscope optical system is also of paramount importance to ensure maximum resolution. The substage condenser must be matched to the objective with respect to numerical aperture and adjustment of the aperture iris diaphragm for accurate light cone formation. The wavelength spectrum of light used to image a specimen is also a determining factor in resolution. Shorter wavelengths are capable of resolving details to a greater degree than are the longer wavelengths. There are several equations that have been derived to express the relationship between numerical aperture, wavelength, and resolution:

Consumers now have the option of a number of different cameras with differently-sized sensors, all at the same price point. Each type of sensor bears both advantages and disadvantages – with such a choice on offer it pays to understand what these are, particularly if you are considering investing in a new model. The following feature looks at these in more detail, and at sensors in general. But first, what exactly is a sensor?

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The most common sensor size in consumer and semi-professional DSLRs, the APS-C sensor applies a crop factor between 1.5x to 1.7x to mounted lenses. It’s also found in Sony compact system cameras, and even some compact cameras.

When light from the various points of a specimen passes through the objective and is reconstituted as an image, the various points of the specimen appear in the image as small patterns (not points) known as Airy patterns. This phenomenon is caused by diffraction or scattering of the light as it passes through the minute parts and spaces in the specimen and the circular back aperture of the objective. The central maximum of the Airy patterns is often referred to as an Airy disk, which is defined as the region enclosed by the first minimum of the Airy pattern and contains 84 percent of the luminous energy. These Airy disks consist of small concentric light and dark circles as illustrated in Figure 3. This figure shows Airy disks and their intensity distributions as a function of separation distance.

Figure 4 illustrates the effect of numerical aperture on the size of Airy disks imaged with a series of hypothetical objectives of the same focal length, but differing numerical apertures. With small numerical apertures, the Airy disk size is large, as shown in Figure 4(a). As the numerical aperture and light cone angle of an objective increases however, the size of the Airy disk decreases as illustrated in Figure 4(b) and Figure 4(c). The resulting image at the eyepiece diaphragm level is actually a mosaic of Airy disks which we perceive as light and dark. Where two disks are too close together so that their central spots overlap considerably, the two details represented by these overlapping disks are not resolved or separated and thus appear as one, as illustrated above in Figure 3.

As sensor is an analogue device, this charge first needs to be converted into a signal, which is amplified before it is converted into a digital form. So, an image may eventually appear as a collection of different objects and colours, but at a more basic level each pixel is simply given a number so that it can be understood by a computer (if you zoom into any digital image far enough you will be able to see that each pixel is simply a single coloured square).

The lenscalculator calculates the Focal length of the lens, based on the desired Field of View (FOV), working distance (WD) and image sensor size.

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The resolution of a microscope objective is defined as the smallest distance between two points on a specimen that can still be distinguished as two separate entities. Resolution is a somewhat subjective value in microscopy because at high magnification, an image may appear unsharp but still be resolved to the maximum ability of the objective. Numerical aperture determines the resolving power of an objective, but the total resolution of a microscope system is also dependent upon the numerical aperture of the substage condenser. The higher the numerical aperture of the total system, the better the resolution.

Careful positioning of the substage condenser aperture diaphragm is also critical to the control of numerical aperture and indiscriminate use of this diaphragm can lead to image degradation (as discussed in the section on substage condensers). Other factors, such as contrast and the efficiency of illumination, are also key elements that affect image resolution.

R Paschotta · 3 — For a defocusing lens (Figure 1b), the focal length is the distance from the lens to the virtual focus (indicated by the dashed lines), taken as a negative ...

The angle µ is one-half the angular aperture (A) and is related to the numerical aperture through the following equation:

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These sensors have become very popular in recent years, especially in premium compact cameras. They offer a sensor which is much larger than a conventional compact camera, but still small enough to fit in pocket friendly devices.

As used in both Four Thirds DSLRs and Micro Four Thirds models, these are roughly a quarter of the size of a full-frame sensor. Their size results in a 2x crop factor, doubling the effective focal length of a mounted lens.

Most objectives in the magnification range between 60x and 100x (and higher) are designed for use with immersion oil. By examining the numerical aperture equation above, we find that the highest theoretical numerical aperture obtainable with immersion oil is 1.51 (when sin (µ) = 1). In practice, however, most oil immersion objectives have a maximum numerical aperture of 1.4, with the most common numerical apertures ranging from 1.0 to 1.35.

When the microscope is in perfect alignment and has the objectives appropriately matched with the substage condenser, then we can substitute the numerical aperture of the objective into equations (1) and (2), with the added result that equation (3) reduces to equation (2). An important fact to note is that magnification does not appear as a factor in any of these equations, because only numerical aperture and wavelength of the illuminating light determine specimen resolution. As we have mentioned (and can be seen in the equations) the wavelength of light is an important factor in the resolution of a microscope. Shorter wavelengths yield higher resolution (lower values for R) and visa versa. The greatest resolving power in optical microscopy is realized with near-ultraviolet light, the shortest effective imaging wavelength. Near-ultraviolet light is followed by blue, then green, and finally red light in the ability to resolve specimen detail. Under most circumstances, microscopists use white light generated by a tungsten-halogen bulb to illuminate the specimen. The visible light spectrum is centered at about 550 nanometers, the dominant wavelength for green light (our eyes are most sensitive to green light). It is this wavelength that was used to calculate resolution values in Table 2. The numerical aperture value is also important in these equations and higher numerical apertures will also produce higher resolution, as is evident in Table 2. The effect of the wavelength of light on resolution, at a fixed numerical aperture (0.95), is listed in Table 3.

Working distancemicroscope

The numerical aperture of an objective is also dependent, to a certain degree, upon the amount of correction for optical aberration. Highly corrected objectives tend to have much larger numerical apertures for the respective magnification as illustrated in Table 1 below. If we take a series of typical 10x objectives as an example, we see that for flat-field corrected plan objectives, numerical aperture increases correspond to correction for chromatic and spherical aberration: plan achromat, N.A. = 0.25; plan fluorite, N.A. = 0.30; and plan apochromat, N.A. = 0.45.

The numerical aperture of a microscope objective is a measure of its ability to gather light and resolve fine specimen detail at a fixed object distance. Image-forming light waves pass through the specimen and enter the objective in an inverted cone as illustrated in Figure 1. A longitudinal slice of this cone of light shows the angular aperture, a value that is determined by the focal length of the objective.

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Used for a number of years in video and stills cameras, CCDs long offered superior image quality to CMOS sensors, with better dynamic range and noise control.

In day-to-day routine observations, most microscopists do not attempt to achieve the highest resolution image possible with their equipment. It is only under specialized circumstances, such as high-magnification brightfield, fluorescence, DIC, and confocal microscopy that we strive to reach the limits of the microscope. In most uses of the microscope, it is not necessary to use objectives of high numerical aperture because the specimen is readily resolved with use of lower numerical aperture objectives. This is particularly important because high numerical aperture and high magnification are accompanied by the disadvantages of very shallow depth of field (this refers to good focus in the area just below or just above the area being examined) and short working distance. Thus, in specimens where resolution is less critical and magnifications can be lower, it is better to use lower magnification objectives of modest numerical aperture in order to yield images with more working distance and more depth of field.

The increased capacity of larger pixels also means that they can contain more light before they are full – and a full pixel is essentially a blown highlight. When this happens on a densely populated sensor, it’s easy for the charge from one pixel to overflow to neighbouring sites, which is known as blooming. By contrast, a larger pixel can contain a greater range of tonal values before this happens, and certain varieties of sensor will be fitted with anti-blooming gates to drain off excess charge. The downside to this is that the gates themselves require space on the sensor, and so again compromise the size of each individual pixel.

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where n is the refractive index of the imaging medium between the front lens of the objective and the specimen cover glass, a value that ranges from 1.00 for air to 1.51 for specialized immersion oils. Many authors substitute the variable α for µ in the numerical aperture equation. From this equation it is obvious that when the imaging medium is air (with a refractive index, n = 1.0), then the numerical aperture is dependent only upon the angle µ whose maximum value is 90°. The sin of the angle µ, therefore, has a maximum value of 1.0 (sin(90°) = 1), which is the theoretical maximum numerical aperture of a lens operating with air as the imaging medium (using "dry" microscope objectives).

Not all pixels on a sensor are used for capturing an image. In fact, those around the peripheries are typically shielded from light, which allows the camera to see how much dark current builds up during an exposure when there is no illumination – this is one of the causes of noise in images. By measuring this, the camera is able to make a rough estimate as to how much has built up in the active pixels, and subtracts this value from them. The result is a cleaner image with less noise.

Parfocal length

With more functionality built on-chip than CCDs, CMOS sensors are able to work more efficiently and require less power to do so, and are better suited to high-speed capture.

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This process creates millions of tiny wells known as pixels, and in each pixel there will be a light sensitive element which can sense how many photons have arrived at that particular location. As the charge output from each location is proportional to the intensity of light falling onto it, it becomes possible to reproduce the scene as the photographer originally saw it – but a number of processes have to take place before this is all possible.

The vast majority of cameras use the Bayer GRGB colour filter array, which is a mosaic of filters used to determine colour. Each pixel only receives information for one colour – the process of demosaicing determines the other two.

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Among the smallest size of sensor used in today’s compacts. While cheaper to manufacture than larger varieties the smaller pixels aren’t quite as efficient, giving rise to noisy images and a reduced dynamic range.

In practice, however, it is difficult to achieve numerical aperture values above 0.95 with dry objectives. Figure 2 illustrates a series of light cones derived from objectives of varying focal length and numerical aperture. As the light cones change, the angle µ increases from 7° in Figure 2(a) to 60° in Figure 2(c), with a resulting increase in the numerical aperture from 0.12 to 0.87, nearing the limit when air is the imaging medium.

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Microlenses help funnel light into each pixel, thereby increasing the sensitivity of the sensor. These are particularly important as a proportion of most sensors’ surface area is taken up by necessary circuitry.

More pixels can mean more detail, but the size of the sensor is crucial for this to hold true: this is essentially because smaller pixels are less efficient than larger ones. The main attributes which separate images from compact cameras (with small sensors) and those from DSLR, CSC or compact camera with a large sensor are dynamic range and noise, and the latter types of camera fare better with regards to each. As its pixels can be made larger, they can hold more light in relation to the noise created by the sensor through its operation, and a higher ratio in favour of the signal produces a cleaner image. Noise reduction technology, used in most cameras, aims to cover up any noise which has formed in the image, but this is usually only attainable by compromising its detail. This is standard on basic cameras and usually cannot be deactivated, unlike on some advanced cameras where the option to do so is provided (meaning you can take more care to process it out later yourself).

These are designed to limit the frequency of light passing through to the sensor, to prevent the effects of aliasing (such as moire patterning) in fine, repetitive details. What results is a slight blurring of the image, which compromises detail, but manufacturers attempt to rectify this by sharpening the image. Many modern sensor designs feature a filter-less design, or a double filter which cancels the effects of the anti-aliasing filter.

This type of sensor was featured in Canon’s older 1D series of cameras. These typically combine the slightly larger sensor with a modest pixel count for speed and high ISO performance, and apply a 1.3x crop factor to mounted lenses. The crop factor was useful for shooting sport and wildlife as it effectively lengthened the lens you were using, but the sensor size has since been discontinued.

Previously, this was usually the largest sensor size you’d find in compact cameras, they’re still bigger than sensors used in budget compacts. This size is relatively rare nowadays, as most manufacturers jump to a one-inch format sensor for their premium offerings.

To this day they are used in budget compacts, but their higher power consumption and more basic construction has meant that they have been largely replaced by CMOS alternatives. They are, however, still used in medium format backs where the benefits of CMOS technology are not as necessary.

Camera sensors are sensitive to some infrared light. A hot mirror in between the lens and the low pass filter prevents this from reaching the sensor, and helps minimise any colour casts or other unwanted artefacts from forming.

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The smaller the Airy disks projected by an objective in forming the image, the more detail of the specimen that becomes discernible. Objectives of higher correction (fluorites and apochromats) produce smaller Airy disks than do objectives of lower correction. In a similar manner, objectives that have a higher numerical aperture are also capable of producing smaller Airy disks. This is the primary reason that objectives of high numerical aperture and total correction for optical aberration can distinguish finer detail in the specimen.

Visitors are invited to explore changes in numerical aperture with changes in µ, using our interactive Java tutorial that investigates how numerical aperture and magnification are related to the angular aperture of an objective.