Concepts

Units

HoloPy does not enforce any particular set of units. As long as you are consistent, you can use any set of units, for example pixels, meters, or microns. So if you specify the wavelength of your red imaging laser as 658 then all other units (x, y, z position coordinates, particle radii, etc.) must also be specified in nanometers.

Coordinate System

For image data (data points arrayed in a regular grid in a single plane), HoloPy defaults to placing the origin, (0,0), at the top left corner as shown below. The x-axis runs vertically down, the y-axis runs horizontally to the right, and the z-axis points out of the screen, toward you. This corresponds to the way that images are treated by most computer software.

Coordinate system used in HoloPy.

In sample space, we choose the z axis so that distances to objects from the camera/focal plane are positive (have positive z coordinates). The price we pay for this choice is that the propagation direction of the illumination light is then negative. In the image above, light travels from a source located in front of the screen, through a scatterer, and onto a detector behind the screen.

More complex detector geometries will define their own origin, or ask you to define one.

Rotations of Scatterers

Certain scattering calculations in HoloPy require specifying the orientation of a scatterer (such as a Janus sphere) relative to the HoloPy coordinate system. We do this in the most general way possible by specifying three Euler angles and a reference orientation. Rotating a scatterer initially in the reference orientation through the three Euler angles \(\alpha\), \(\beta\), and \(\gamma\) (in the active transformation picture) yields the desired orientation. The reference orientation is specified by the definition of the scatterer.

The Euler rotations are performed in the following way:

  1. Rotate the scatterer an angle \(\alpha\) about the HoloPy \(z\) axis.
  2. Rotate the scatterer an angle \(\beta\) about the HoloPy \(y\) axis.
  3. Rotate the scatterer an angle \(\gamma\) about the HoloPy \(z\) axis.

The sense of rotation is as follows: each angle is a rotation in the clockwise direction about the specified axis, viewed along the positive direction of the axis from the origin. This is the usual sense of how rotations are typically defined in math:

Matrix equation for Euler rotations.