Digital Camera Resolution Requirements for Optical Microscopy

The ultimate resolution of a charge-coupled device (CCD) or complementary metal oxide semiconductor (CMOS) image sensor is a function of the number of photodiodes and their size relative to the image projected onto the surface of the imaging array by the microscope optical system. When attempting to match microscope optical resolution to a specific digital camera and video coupler combination, use this calculator for determining the minimum pixel density necessary to adequately capture all of the optical data from the microscope.

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The tutorial initializes with a randomly chosen specimen appearing in the Specimen Image window (black box) and bounded by the eyepiece aperture or projection lens field diaphragm. A colored rectangle designating the CCD dimensions (2/3-inch by default) is superimposed over the image to reveal the actual area of the specimen that is captured by the sensor. In the gray, yellow, and red boxes beneath the sliders, the microscope Optical Resolution (gray), CCD Required Pixel Size (yellow), Optimum CCD Array Size (yellow), Monitor Magnification (red) and Total Magnification (red) of the image are presented in micrometers or a product. These values are continuously updated as the sliders are translated. A new CCD Format (size) can be selected by using the radio buttons appearing to the left of the Specimen Image window. The physical CCD Dimensions of the selected sensor (in millimeters) are displayed on the right side of the image window along a rectangle having the same aspect ratio as the imaging chip.

In order to operate the tutorial, shift the Numerical Aperture and Objective Magnification sliders (values appear above the slider bars) to set the appropriate values for the microscope optical configuration to be considered. Next, choose an eyepiece or projection lens Field Number (values range between 18 and 26 millimeters) and Video Coupler magnification (between 0.5x and 1.0x). As the coupler slider is translated, the size of the rectangle superimposed over the specimen image is altered by the tutorial to match the specimen area captured by the CCD sensor. A new specimen can be selected at any point by using the Choose A Specimen pull-down menu.

The efficiency of capturing images generated by an optical microscope onto the photodiode array of a CCD or CMOS image sensor is dependent upon several factors, ranging from the objective magnification, numerical aperture, and resolution, to the electronic image sensor photodiode array size, aspect ratio, video coupler magnification, and the dimensions of individual photo-sensitive elements within the array. In addition, parameters that are specific to the specimen being imaged, such as contrast, signal-to-noise ratio, intrascene dynamic range, and integration time, must also be considered.

The ultimate optical resolution of a CCD is a function of the number of photodiodes and their size relative to the image projected onto the array surface by the microscope lens system. Currently available CCD arrays vary in size from several hundred to many thousands of pixels. Modern array sizes used in devices intended for scientific investigations range from 1000 × 1000 up to 5000 × 5000 sensor elements. The trend in consumer and scientific-grade CCD manufacture is for the sensor size to continuously decrease, and digital cameras with photodiodes as small as 4 × 4 micrometers are currently available.

Adequate resolution of a specimen imaged with the optical elements of a microscope can only be achieved if at least two samples are made for each resolvable unit, although many investigators prefer three samples per resolvable unit to ensure sufficient sampling. In diffraction limited optical instruments, such as the microscope, the Abbe limit of optical resolution at an average visible light wavelength (550 nanometers) is 0.20 micrometers when using an objective lens having a numerical aperture of 1.4. In this case, a sensor size of 10 square micrometers would be just large enough to allow the optical and electronic resolution to be matched, with a 7 × 7 micrometer sensor size preferred. Although smaller photodiodes in a CCD image sensor improve the spatial resolution, they also limit the dynamic range of the device.

Pixel Size Requirements for Matching Microscope Optical Resolution
Objective
(Numerical Aperture)
Resolution
Limit
(Micrometers)
Projected
Size
(Micrometers)
Required Pixel
Size
(Micrometers)
1x (0.04) 6.9 6.9 3.5
2x (0.06) 4.6 9.2 4.6
2x (0.10) 2.8 5.6 2.8
4x (0.10) 2.8 11.2 5.6
4x (0.12) 2.3 9.2 4.6
4x (0.20) 1.4 5.6 2.8
10x (0.25) 1.1 11.0 5.5
10x (0.30) 0.92 9.2 4.6
10x (0.45) 0.61 6.1 3.0
20x (0.40) 0.69 13.8 6.9
20x (0.50) 0.55 11.0 5.5
20x (0.75) 0.37 7.4 3.7
40x (0.65) 0.42 16.8 8.4
40x (0.75) 0.37 14.8 7.4
40x (0.95) 0.29 11.6 5.8
40x (1.00) 0.28 11.2 5.6
40x (1.30) 0.21 8.4 4.2
60x (0.80) 0.34 20.4 10.2
60x (0.85) 0.32 19.2 9.6
60x (0.95) 0.29 17.4 8.7
60x (1.40) 0.20 12.0 6.0
100x (0.90) 0.31 31.0 15.5
100x (1.25) 0.22 22.0 11.0
100x (1.30) 0.21 21.0 10.5
100x (1.40) 0.20 20.0 10.0
Table 1

In microscopy, the image is typically projected by the optical system onto the surface of a detector, which can be the retina of a human eye, an electric image sensor, or the sensitive chemical emulsion on traditional film. In order to optimize the information content of the resulting image, the resolution of the detector must closely match that of the microscope. The wavelength spectrum of visible light used to create the image of a specimen is one of the determining factors in the performance of the microscope with respect to optical resolution. Shorter wavelengths (375-500 nanometers) are capable of resolving details to a greater degree than are the longer wavelengths (greater than 500 nanometers). The limits of spatial resolution are also dictated by the diffraction of light through the optical system, a term that is generally referred to as diffraction limited resolution. Investigators have derived several equations that have been used to express the relationship between numerical aperture, wavelength, and optical resolution:

(1)
r = λ/(2 × NA)

(2)
r = 0.61 × λ/NA

(3)
r = 1.22 × λ/(NAObj + NACond)

Where r is resolution (the smallest resolvable distance between two specimen points), NA equals the objective numerical aperture, λequals 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. The assumption is that two point light sources can be resolved (separately imaged) when the center of the Airy disk generated by one of the sources overlaps with the first order reflection in the diffraction pattern of the second Airy disk, a condition known as the Rayleigh Criterion. In some instances, such as confocal and multiphoton 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 0.20 microns using a mid-spectrum wavelength of 550 nanometers) and a numerical aperture of 1.35 to 1.40 are not realized in practice.

When the microscope is in perfect alignment and has the objectives appropriately matched with the substage condenser, then objective numerical aperture value can be substituted into equations (1) and (2), with the added result that equation (3) reduces to equation (2). An important concept to note is that magnification does not appear as a factor in any of these equations, because only numerical aperture and the wavelength of the illumination determine specimen resolution. As mentioned above (and can be observed 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 vice 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 broad-spectrum 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 for the tutorial and presented in Table 1. The numerical aperture value is also important in these equations and higher numerical apertures will also produce higher resolution (see Table 1).


Contributing Authors

Matthew J. Parry-Hill, Kimberly M. Vogt, John D. Griffin, and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.