-10-
2.2.3
Optical Considerations
A typical optical system can be represented as below.
Figure 2: Field of View
Using above notations:
The sensor size depends on frame dimension:
𝑺𝒆𝒏𝒔𝒐𝒓 𝑺𝒊𝒛𝒆 = 𝑺 = 𝑷𝒊𝒙𝒆𝒍𝑺𝒊𝒛𝒆 × √𝑹𝒆𝒔𝒐𝒍𝒖𝒕𝒊𝒐𝒏_𝑿
𝟐
+ 𝑹𝒆𝒔𝒐𝒍𝒖𝒕𝒊𝒐𝒏_𝒀
𝟐
To select a lens, you can use above formula:
𝑭𝒐𝒄𝒂𝒍 𝑳𝒆𝒏𝒈𝒕𝒉 = 𝑭𝑳 =
𝑾𝑫
𝟏+
𝑭𝒐𝑾
𝑺
(distances in millimeters, mm)
Alternatively, if you already have a lens, you can compute working distance using above formula:
𝑾𝒐𝒓𝒌𝒊𝒏𝒈 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 = 𝑾𝑫 = 𝑭𝑳 × (𝟏 +
𝑭𝒐𝑾
𝑺
)
(distances in millimeters, mm)
Examples:
•
PixelSize = 0.008mm
•
Full resolution 1696 x 1708
•
FoW = Object size = 100 mm
•
WD = 300 mm
𝑆 = 0,008 × √1696
2
+ 1708
2
= 19,26
𝐹𝐿 =
300
1 +
100
19,26
~48,5 𝑚𝑚
Selected focal length = 50 mm.
Same example but using a 35mm lens.
𝑊𝐷 = 35 × (1 +
100
19,26
) ~217 𝑚𝑚
Object must be set at least at WD = 217 mm.
