Resolution is a measurement of an imaging system’s ability to reproduce object detail. The smaller the object detail, the higher the required resolution.

To determine the absolute minimum resolvable spot that can be seen on the object, the ratio of the filed of view to sensor size needs to be calculated. This is also known as the Primary Magnification (PMAG) of the system.

$$ \text{PMAG}=\frac{\text{sensor size (mm)}}{\text{field of view (mm)}} $$

Known parameters:

Pixel size: 15 µm $\times$ 15 µm

Number of pixels (Horizontal $\times$ Vertical): 640 $\times$ 512 → 9.6 mm $\times$ 7.68 mm

Desired FOV (Horizontal): 27 mm

Limiting sensor resolution:

At first, we need to understand a line pair in the sensor. It consists of one dark line and one bright line, representing the smallest distinguishable pattern by the sensor.

Typically, the resolution is defined by the frequency measured in line pairs per millimeter (lp/mm)

$$ \text{image space resolution}=\frac{1000\mu m/mm}{2 \times\text{pixel size }\mu m}=\frac{1000\mu m/mm}{2 \times15}=33.3 \text{lp/mm} $$

Next, the ratio of the FOV to the sensor size is calculated. This is also known as Primary Magnification (PMAG)

$$ \text{PMAG}=\frac{9.6}{27}\approx0.36X $$

→ Therefore the lens should be choose at the range 0.36X

Now, to calculate the resolution of image, we should

$$ \text{object space resolution}=0.36\times33.3=11.988\ \text{lp/mm}\approx 41 \mu m $$