In Volocity, Point Spread Functions (PSFs) are calculated in object space, also referred to as the back-projected plane or specimen plane. This approach ensures that PSFs remain independent of magnification, as they are applied based on the physical dimensions of the images being deconvolved. This eliminates the need to manually input the magnification parameter when calculating the PSF, provided the image calibration is correctly set.

PSF Considerations for Spinning Disk Confocal Systems

For spinning disk confocal systems, the calculation of PSFs must account for the interference pattern caused by the multiplicity of pinholes in the spinning disk. The following key factors are involved:

1. Back-Projected Pinhole Size and Spacing:

   • The physical size and spacing of the pinholes in the spinning disk must be projected back to the sample plane, considering all magnification components between the spinning disk and the sample.
   • Typical parameters for a spinning disk include:
     • Disk spacing: 250 µm
     • Pinhole size: 50 µm
   • For a 100X objective lens, these values project to:
     • Distance between pinholes: 2.5 µm
     • Pinhole size: 0.5 µm

2. Intermediate Magnification (Optivar):

   • If an Optivar is positioned between the spinning disk and the physical sample, its magnification must be included in the calculation of the back-projected pinhole size and spacing.
   • For example, if a 1.6x Optivar is used with a 100X objective lens, the total magnification becomes:
     • Total Magnification = Objective Magnification × Optivar Magnification
     • Total Magnification = 100 × 1.6 = 160X
   • However, intermediate magnification components that lie outside the optical path between the spinning disk and the sample should not be included in this calculation.

3. Numerical Aperture (NA) Considerations:

   • When an Optivar is added, it effectively creates a new lens system composed of the objective and the Optivar.
   • The focal length (f) of this new system is reduced by the Optivar magnification (M), while the size of the entrance aperture remains unchanged.
   • At small angles, the Numerical Aperture (NA) is calculated as:
     NA = f / Radius of the Entrance Aperture
   • Adding the Optivar reduces the focal length without changing the entrance aperture, causing the NA to decrease.
   • For example, if a 1.6x Optivar is used, the NA must also be divided by 1.6.

Calculating PSFs in Volocity

If you choose the Calculated PSF option in Volocity, you must manually account for the additional magnification introduced by the Optivar and adjust the NA accordingly:

1. Total Magnification:

   • Multiply the objective magnification by the Optivar magnification.
   • Example:
     Total Magnification = 100 × 1.6 = 160X

2. Adjusted NA:

   • Divide the original NA of the objective lens by the Optivar magnification.
   • Example:
     Adjusted NA = Original NA ÷ 1.6

Verifying the Pinhole Size and Spacing

To physically verify the pinhole size and spacing:

1. Stop the spinning disk and measure the pattern in the image plane.
2. For a 100X objective lens:
   • Disk spacing: 250 µm back-projects to 2.5 µm.
   • Pinhole size: 50 µm back-projects to 0.5 µm.

Conservation of Etendue and NA Limitations

Adding an Optivar introduces a physical limitation due to the conservation of etendue, which governs the trade-off between magnification, aperture size, and light throughput. For more information on this topic, consult relevant optical theory resources.

By carefully accounting for intermediate magnification and the adjusted NA, you can ensure accurate PSF calculations for deconvolving data acquired with spinning disk confocal systems.