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These cameras typically use Nikon bayonet (F-mount) or M42 to M72 as lens connections. Only then high-resolution sensors with large pixels can be used in order to build line scan cameras with up to 12k pixels or area scan cameras with up to 28 million pixels.

Often times when starting the design process one can inadvertently request conflicting specifications. This example will show how easy this is to do and how to avoid it when specifying a lens.

This specification describes how many electrons a pixel element can hold before it is completely saturated. A pixel of 5.5 μm structure size can accumulate approximately 20,000 electrons, a 7.4 μm pixel 40,000 electrons.

Important: If you have the choice between a larger and a smaller sensor for the same camera version, please take the larger variant if you…

Numerical apertureof objective lens

This is an exact equation relating the NA to the f/#, but it is often convenient to have an approximation for this. When n = 1 (medium is air) and if we use a small angle approximation (sin α ≈ tan α) then:

In order to equate NA and f/#, we can use simple geometric relationships. Figure 3.1 shows a simple lens focusing light rays (blue lines) from infinity to a point. This creates a cone of light that can be described by numerical aperture using the previous equation. The half angle, α, can now be defined by the following equation:

Numerical apertureformula

Now that we have briefly explained what numerical aperture is, we can equate it to f/#. As explained here, f/# is also a measure of how much light can get through a lens. f/# of a simple lens is defined by the following equation, where f is the focal length of the lens and D is the diameter (or more specifically the entrance pupil diameter for more complex lens systems).

Numerical aperture definitionphysics

So what if the customer needs a numerical aperture of 0.25? To get this, at least one of the other specifications need to change. To do this, lets start with the initial specification for NA=0.25 and find what the f/# would be using this spec.

Industrial cameras usually use 1/3" sensors in case of resolutions of 640 x 480 pixels, cameras with 1280 x 1024 pixels mainly 1/2". The quite popular camera resolution of 1600 x 1200 pixels often uses a somewhat larger sensor with 1/1.8" with the same pixel size.

To determine whether lens specifications are compatible, we need to find the resulting numerical aperture from the other three specifications. To do this we will first need to use the equation below to relate the image height h, focal length f and the half field of view Θ. This equation can be derived using simple geometry using the relationships shown in the red triangle in figure 3.2.

Numerical apertureof microscope

The sensors used in standard cameras are clearly smaller and range from 4 to 16 mm image diagonal. These sensor sizes, too, are indicated in inches. The 1-inch sensor has a diagonal of 16 mm.

The advancing technological development of CCD and CMOS sensors allows for the production of finer and finer semiconductor structures. As a general trend, sensor and pixel sizes shrink in order to cut more and more sensors out of one wafer. This is possible because the sensitivity of the pixels increasingly enhances, too, as much as the noise performance of the electronics is being optimised.

If the medium is not air, as is common for some microscope objectives, the approximation above can be multiplied by the index of refraction of the medium as shown below.

The inch data of the CCD and CMOS sensors only have a historic explanation: pick-up tubes of TV cameras were used up to the mid-1980s and were long superior to CCD or CMOS sensors which were invented in the late 1960s.

The actual image converter of the tube cameras was located in a glass vacuum tube, and the different pick-up tubes were, among other things, classified according to their outer diameter of the glass bulb. The diagonal of the light-sensitive surface within the tube was of course smaller and represented approximately two thirds of the outer diameter. Equivalent CCD sensors which are supposed to replace the cathode-ray tubes had to cover exactly this surface. A CCD the light-sensitive surface of which corresponds to a 1/2-inch tube was therefore called 1/2-inch sensor, even if this does not correspond to the real CCD sensor size.

Pixels with an edge length of 14 or 10 μm are preferentially used in line scan cameras. Due to the high line frequency of 18 Hz, for instance, the maximum exposure time is 1000/18000 = 55 μs for one captured image line. The light-active surface of the pixel can never be large enough in this case.

Numerical apertureunit

A line scan camera with 2048 pixels with 10 μm pixel sizes has a line length of 10.48 mm, in case of 14 μm pixel size the sensor is already 28.6 mm long. From 20 mm sensor diagonal on, the C-mount lens connection can no longer be used.

Now we can find the focal length of the lens by assuming that the customer wants entrance pupil diameter to stay at the specified 20mm.

Numerical apertureof optical fiber

The larger the full well capacity, yet the better the maximum signal-noise ratio. Consumer cameras with pixel sizes of 1.7 μm require only about 1,000 photons for the pixel saturation. In case of digitalisation with 8, 10, or even 12 bits, other noise effects (photon noise, digitalisation noise, dark noise) can already assume significant scales, interfere with the signal and thus influence the image in an extremely negative way.

Numerical aperture definitionin optical

In general there is the trend that the sensors become smaller and smaller on the mass camera market. If a standard VGA sensor had, in some cases, a size of 2/3" in the late 1980s, it is only 1/3" today. The miniaturisation is a consequence of enhanced production processes which allow for smaller light-sensitive surfaces with a (hopefully) similar performance. It enables the manufacturers to produce a larger number of sensors at a lower price from one wafer. A 1/3" sensor, for example, has only approximately 40% of the surface of a 1/2" sensor and is therefore cheaper.

Below are three sets of lens specifications that would result in the desired system NA. There is an infinite number of specifications that will give the desired NA if one is allowed to change more than one spec.

In case of high-resolution area scan or line scan cameras, significantly larger sensors with a size of several centimetres are used. The dimensions of these sensors are normally not standardised and result from the resolution and pixel sizes of the sensors. Everything is permitted and only limited by the budget.

As a consequence of the miniaturisation of sensors, the pixel sizes grow smaller and smaller. Sensors of consumer cameras (8 to 12 megapixels for 200 euros) have pixel sizes of mostly 1.7 μm today, the light-active surface per pixel is therefore only approximately 3 μm2. This results in an extremely strong sensor noise in case of non-optimal lighting conditions. For quality control using cameras, this is absolutely inacceptable.

Numerical apertureof lens

Machine vision cameras (C-mount) with resolutions from VGA to 2 megapixels normally have pixels of 4.6 to 6.5 μm with a 10 - 15 times larger light-active surfaces and thus clearly better signal results. If you need images as noise-free as possible and precise measuring results, look for preferably large sensor pixels, even if these cameras are more expensive!

Numerical aperture (NA) refers to the cone of light that is made from a focusing lens and describes the light gathering capability of the lens (similar to f/# ). NA is defined by the following equation, where n is the index of refraction of the medium (often n=1 for air), and α is the half angle of the cone of light exiting the lens pupil.

As technical limits are reached in this respect, too, it is worthwhile to compare cameras with different sensor and pixel sizes with the same resolution, especially if…

Classic machine vision cameras have varyingly large sensors, depending on the camera and resolution used. The majority of cameras with smaller sensors are used with so-called C-mount or possibly CS-mount optics. The C-mount thread has an actual diameter of 1 inch, i.e. 25.4 mm and a thread pitch of 1/32 inch.

A larger sensor with larger pixels is in almost every case the technically better choice, however, the price is always higher.