Sample Datasets

Hezaveh uses $192\times192$ image size with a pixel size of 0.04" (seconds of arc). This seems to be a reasonable choice to follow.

Proposed Selection Algorithm¶

This is based on a sketch by Ben David March 2026.

1. Choose the Einstein radius uniformly at random, so that $0.1"\le\theta_E\le3.0"$.

   • where $\theta_E=R_E/\chi$, i.e. $R_E$ converted to angular units.

2. Choose the source position inside or around the critical curve, For example, choose the polar coordinates $(R,\phi)$

   • so that $R\le c\theta_E$ for some constant $C$, e.g. $c=1.2$.

   • $\phi$ chosen uniformly at random

3. Choose the orientation of the elliptical lens uniformly at random from a half-circle.

4. Choose the orientation of the elliptical source uniformly at random from a half-circle.

5. CHoose the ellipticity $f$ of the lens uniformly at random, so that $0.1\le f\le 0.9$.

6. Source parameters - sersic profile

   • size: $0.04"\le\sigma\le0.2"$

   • sersic index $1\le n_s\le 5$

   • luminosity $10\le l\le 20$, exponentially distributed with $\lambda=2.0$ (see below)

Cluster lenses¶

1. For cluster lenses, each constituent lens is placed in the same way as the source, relative to the origin, in polar co-ordinates $(R_L,\phi_L)$.

   • select random distance $R_L\le2\theta_E$, where $\theta_E$ is the Einstein radius of the constituent lens

   • select random angle $\phi_L$

Proposal from Oda¶

The exponential distribution used for luminsoty returns $u = 1 - \exp{-\lambda\cdot x}$ where $x$ is exponentially distributed, that is with a probability density function $f(x;\lambda) = \lambda\exp{-\lambda x}$ for positive $x$.
This $u$ is scaled to within the given range.