Section 2: Understanding Lens Specifi cations
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Understanding a manufacturer’s speci cations for a lens can greatly
simplify the research and purchasing processes. In order to know how
a lens works, it is critical to understand resolution, magni cation, contrast,
f/#, and how to read common performance curves including
Modulation Transfer Function (MTF), Depth of Field (DOF), Relative
Illumination, and distortion.
Section 2.1: Resolution
Resolution is a measurement of an imaging system’s ability to reproduce
object detail and can be in uenced by factors such as the type
of lighting used, the pixel size of the sensor, or the capabilities of the
optics. The smaller the object detail, the higher the required resolution.
Dividing the number of horizontal or vertical pixels on a sensor into
the size of the object one wishes to observe will indicate how much
space each pixel covers on the object and can be used to estimate resolution.
However, this does not truly determine if the information on the
pixel is distinguishable from the information on any other pixel.
As a starting point, it is important to understand what can actually
limit system resolution. An example can be shown in Figure 2.1: a pair of
squares on a white background. If the squares are imaged onto neighboring
pixels on the camera sensor, then they will appear to be one
larger rectangle in the image (a) rather than two separate squares (b).
In order to distinguish the squares, at least one pixel needs to be between
them. This minimum distance is the limiting resolution of the
system. The absolute limitation is de ned by the size of the pixels on
the sensor as well as the number of pixels on the sensor.
The Line Pair and Sensor Limitations
The relationship between alternating black and white squares is often
described as a line pair. Typically, the resolution is de ned by the
frequency measured in line pairs per millimeter (lp/mm). A lens’s resolution
is unfortunately not an absolute number (learn more in Section
3). At a given resolution, the ability to see the two squares as separate
entities will be dependent on grey scale level. The bigger the separation
in the grey scale between the squares and space between them
(Figure 2.1b), the more robust is the ability to resolve the squares. This
grey scale separation is known as contrast (at a speci ed frequency).
The spatial frequency is given in lp/mm. For this reason, calculating
resolution in terms of lp/mm is extremely useful when comparing
lenses and for determining the best choice for given sensors and applications.
Contrast is explained in more detail in Section 2.3.
The sensor is where the system resolution calculation begins. By
starting with the sensor, it is easier to determine what lens performance
is required to match the sensor or other application requirements.
The highest frequency which can be resolved by a sensor, the
Nyquist frequency, is e ectively two pixels or one line pair. Table
2.1 shows the Nyquist limit associated with pixel sizes found on some
highly used sensors. The resolution of the sensor, also referred to as
the image space resolution for the system, can be calculated by multiplying
the pixel size in μm by 2 (to create a pair), and dividing that into
1000 to convert to mm:
sensor resolution = image space resolution = 1000 μm/mm
in lp/mm in lp/mm 2 x pixel size (μm)
Sensors with larger pixels will have lower limiting resolutions. Sensors with
smaller pixels will have higher limiting resolutions. How this information is
used to determine necessary lens performance can be found in Section 3.
With this information, the limiting resolution on the object to be
viewed can be calculated. In order to do so, the relationships between
Figure 2.1 Camera Resolution Limit
the sensor size, the eld of view, and the number of pixels on the sensor
need to be understood.
Sensor size refers to the size of a camera sensor’s active area, typically
speci ed by the sensor format size (Page 149). However, the exact sensor
proportions will vary depending on the aspect ratio, and the nominal
sensor formats should be used only as a guideline, especially for telecentric
lenses and high magni cation objectives. The sensor size can be
directly calculated from the pixel size and the number of active pixels on
Horizontal sensor = (Horizontal pixel size in μm) x (# of active horizontal pixels)
dimension in mm 1000 μm/mm
(Vertical pixel size in μm) x (# of active vertical pixels)
dimension in mm 1000 μm/mm
Pixel Size (μm) Associated Nyquist Limit (lp/mm)
Table 2.1: As pixel size increases, the associated Nyquist limit in lp/mm
Figure 2.1: Resolving two squares. If the space between the squares
is too small (a) the camera sensor will be unable to resolve them as