FOV and speed calculator

Use this calculator when selecting a lens, estimating the field of view, checking depth of field (DoF), or matching camera frame rate to scanner or conveyor speed. For push-broom HSI, the scan direction is built line by line, so belt speed, frame rate, exposure, slit size, spatial resolution, and focus depth all affect whether the resulting datacube has the expected proportions and sharpness.

Selecting appropriate lens

• All qtec camera heads are made with the C-mount type lens mount.
• Check the sensor list in order to determine the required lens size (based on sensor size)
  • fx: 1/2" (IMX990) or 1/4" (IMX991)
• Remember to select a lens with the appropriate resolution (pixel size)
  • A low resolution lens can result in the blurring of pixels

Calculating FOV and framerate

• Desired field of view (FOV) or pixel/mm resolution
• Desired working distance
• Aperture and acceptable circle of confusion for estimating depth of field
• Sensor size (image and pixel sizes)
• Slit size for spectrograph (default: 20um)

Depth of field

Depth of field estimates how much height variation can stay acceptably sharp at the selected working distance, focal length, aperture, and circle of confusion. This matters for scanner setups where samples are not perfectly flat or where a translation stage, belt, or tray introduces height variation across the scan.

A circle of confusion of 2 px is used by default as a compromise between a strict sharpness requirement and the wider spatial footprint of the slit. Use 1 px for a more conservative estimate that preserves the finest spatial detail. For the HV 1700 with 5 um pixels and a 20 um slit, use 4 px if blur up to the width of the slit is acceptable. A larger circle of confusion produces a larger DoF estimate; it changes the accepted blur tolerance, not the camera optics.

A longer focal length or a wider aperture (a smaller F-number) gives a shallower DoF. Making the aperture opening smaller (selecting a larger F-number) increases the DoF, but also reduces the amount of light reaching the sensor.

For the HV 1700, F/2.8 is the widest supported aperture. Do not open the lens wider than F/2.8, because the spectrograph can then produce optical artefacts and stray light effects. If more depth of field is needed, the lens may be closed to a larger F-number. This increases the DoF, but reduces the light reaching the sensor, so illumination and exposure time may need to be adjusted.

Formulas

• focal_length[mm] / sensor_size[mm] = distance_to_object[mm] / field_of_view[mm]
• sensor_size[mm] = sensor_size[px]*pixel_size[um]*1000
• resolution[mm/px] = field_of_view[mm] / sensor_size[px]
• field_of_view[deg] = 2 * atan2(sensor_size[mm]/2, focal_length[mm]) * 180/PI
• sensor_size_y[px] = slit_size[um] / pixel_size[um]
• framerate = 1 / (resolution[mm/px] / belt_speed[mm/s]) for keeping aspect ratio
• framerate = 1 / (sensor_size_y[px] * resolution[mm/px] / belt_speed[mm/s]) for 1 to 1 sampling
• motion_blur[mm] = belt_speed[mm/s] * exp_time[s]
• motion_blur[px] = motion_blur[mm] / resolution[mm/px]
• depth_of_field[mm] = 2 * distance_to_object[mm]² * aperture[N] * circle_of_confusion[mm] / focal_length[mm]²
• max_bands[lines] = (1/fps - B) / A, where A and B depend on the sensor type and bit mode

HV1700 wavelength helpers

For a full-range HV1700 datacube with 900 indexed bands covering 430-1700 nm, use these approximations to move between wavelength and band index:

• band_index = round((wavelength_nm - 430) * 899 / (1700 - 430))
• wavelength_nm = 430 + band_index * (1700 - 430) / 899

Common visible preview bands are approximately:

Channel	Wavelength	Band index
Red	620 nm	134
Green	530 nm	71
Blue	450 nm	14

These are useful starting points for false RGB previews. If the datacube has wavelength metadata, HV Explorer can also use wavelength-based presets directly.