What Is the Thin Lens Imaging & Rayleigh Resolution Calculator?
Thin lens imaging determines image position and scale, while the Rayleigh criterion defines the diffraction-limited resolution of the lens.
How Does the Thin Lens Imaging & Rayleigh Resolution Calculator Work?
Combines the Gaussian lens equation with the Fraunhofer circular aperture diffraction Bessel function null.
Thin Lens Imaging & Rayleigh Resolution Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
rac{1}{f} = rac{1}{d_o} + rac{1}{d_i}, quad m = - rac{d_i}{d_o}, quad r_{ ext{Airy}} = 1.22 lambda left( rac{f}{D}
ight)
Thin lens Gaussian formula combined with Rayleigh diffraction limit.
How to Use the Thin Lens Imaging & Rayleigh Resolution Calculator
- Input focal length, object distance, entrance aperture diameter, and light wavelength.
Step-by-Step Example Calculation
Camera 50mm Prime Lens at f/2.0
Input Values:
focalLengthMm:50
objectDistanceMm:500
lensApertureDiameterMm:25
wavelengthNm:550
Worked Steps: Forms image at d_i = 55.56 mm with magnification -0.111x and Airy disk radius 1.34 µm.
Understanding Your Result
Airy disk radius defines the smallest spot diameter resolvable by the optical sensor pixels.
Factors That Affect the Result
- Stopping down a lens increases depth of field but increases the Airy disk size (diffraction softening).
When Should You Use This Calculator?
- Telescope aperture sizing, microscope objective selection, machine vision camera sensor matching.
Assumptions & Limitations
- Assumes paraxial approximation and aberration-free (diffraction-limited) optics.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Rayleigh diffraction limit for circular apertures.