In optical imaging systems, image contrast performance is most commonly specified using the Modulation Transfer Function (MTF) at one or more critical spatial frequencies. While full MTF curves are invaluable for final validation, they are often poorly behaved during early optimization, making direct MTF-based optimization slow and unstable.
To overcome this, Zemax OpticStudio provides an advanced method called Optical Image Contrast Optimization, which enables robust and efficient optimization of MTF at a specified spatial frequency.
The Challenge with Direct MTF Optimization
During early design stages:
- Aberrations are large
- MTF values fluctuate sharply
- Gradients are noisy or discontinuous
As a result, directly optimizing the MTF:
- Converges slowly
- Easily becomes trapped in local minima
- Often fails until the design is already near-final
What Is Optical Image Contrast Optimization?
Instead of calculating the full MTF, Contrast Optimization works by:
- Measuring wavefront phase differences in the exit pupil
- Comparing pairs of rays separated by a pupil shift corresponding to the desired spatial frequency
- Minimizing these wavefront differences to maximize contrast
In short: Reducing OPD differences between properly spaced rays directly increases the MTF at the target spatial frequency.
This approach is:
- Faster
- More stable
- Better behaved than direct MTF optimization
In this example, the imaging system must meet the following requirement:
MTF ≥ 40% @ 20 lp/mm across full field
System Constraints
- Wavelength range: 440 – 770 nm (visible)
- Entrance pupil diameter: 44 mm
- Target system speed: F/3
- Starting design: plane-parallel plates
- F-number enforced using a radius solve on the final surface
Using the Merit Function Wizard:
Select Image Quality Criterion: Contrast
Specify the spatial frequency of interest (20 lp/mm)
Define the relative weighting between:
Sagittal MTF
Tangential MTF
The wizard automatically generates a merit function using MECS and MECT operands.
Understanding MECS and MECT Operands
These operands are designed to work in pairs:
MECS (Sagittal Contrast)
Traces three rays:
One unshifted ray
One ray shifted by d in the sagittal pupil direction
One ray shifted by d in the tangential direction
Reports optical path difference (OPD) in waves for the sagittal ray pair
MECT (Tangential Contrast)
Reports OPD for the tangential ray pair
The value of d corresponds directly to the target spatial frequency in the MTF.
Driving both MECS and MECT values toward zero:
- Equalizes wavefront phase
- Maximizes contrast at the specified spatial frequency
The remaining radii of curvature and spacings were set to variables for a Damped Least Squares optimization.
After 20 seconds optimization, the layout and image contrast by MTF is shown as below:
We continue to run the optical image contrast optimization by hammer optimization for 20 hours.
Optimization Results
After initial DLS optimization:
- Layout becomes well structured
- MTF contrast improves rapidly
After Hammer Optimization:
- MTF exceeds 40% at 20 lp/mm
- Performance is consistent across the full field
- The solution is more robust than direct MTF-based designs
Why Contrast Optimization Works Better
- Avoids unstable full MTF calculations
- Uses smooth, well-behaved OPD metrics
- Converges faster in early design stages
- Targets specific, application-critical spatial frequencies
- Scales well to broadband and wide-field systems
This makes Optical Image Contrast Optimization ideal for:
- Camera lenses
- Machine vision optics
- Fluorescence and biomedical imaging
- Surveillance and inspection systems
References