In optical metrology, the choice between standard entocentric lenses and telecentric lenses is one of the most critical decisions affecting measurement system variation. This guide compares their physical optical behaviors and outlines when telecentricity is required.
1. Physical Behavior of Entocentric Lenses
Standard imaging lenses are entocentric. This means their chief rays diverge from the lens entrance pupil. As a result:
- Objects closer to the lens appear larger; objects farther away appear smaller.
- The field of view is angular, resembling a cone.
- Parallax Error: If an object has significant height or depth (such as a cylinder viewed from the top), the sides of the object are visible in the image corners. This makes it difficult to measure the top face diameter accurately if the part’s axial placement varies.
2. Physical Behavior of Telecentric Lenses
Telecentric lenses restrict the light paths such that the chief rays are parallel to the optical axis. This is achieved by placing an aperture stop at the back focal point of the objective lens.
Telecentricity can be:
- Object-Space Telecentric: Chief rays are parallel on the object side. This eliminates change in magnification due to object distance variation.
- Image-Space Telecentric: Chief rays are parallel on the sensor side, ensuring uniform light landing angles on the sensor pixels.
- Bi-telecentric: Telecentric on both object and image spaces, offering the highest performance for metrology.
Key Benefits for Precision Metrology
- Constant Magnification: Within a specific range of depth (the telecentric depth), a part can shift closer to or farther from the lens without changing its measured size in pixels.
- Zero Parallax Error: Features at different heights line up perfectly. A cylinder’s top and bottom faces align, allowing pure 2D profile inspection.
- Uniform Illumination: Bi-telecentric designs ensure high radiometric uniformity across the sensor plane, minimizing edge detection shifts due to brightness fall-off.
3. Comparative Performance Metrics (Synthetic Baseline)
Below is a comparison of typical behaviors under simulated axial part displacement ($z$-shift):
| Optical Parameter | Standard Entocentric Lens | Object-Space Telecentric Lens |
|---|---|---|
| Field of View Shape | Conical (Angular) | Cylindrical (Parallel) |
| Magnification Sensitivity to $z$-shift | High (follows $M \propto 1/z$) | Low (bounded by telecentric slope, e.g., $<0.1%$) |
| Parallax/Perspective | Visible (edges tilt outwards) | Eliminated (within telecentric range) |
| Average Physical Size | Compact, light | Large (front element diameter must exceed FoV) |
| Cost Profile | Economical | Premium |
Assumptions and Design Constraints
- Telecentric Range Limits: Constant magnification is only maintained within the lens’s rated depth of field (or telecentric range). Shifting beyond this range will cause optical defocus, though the centroid of the blur may remain geometrically stable.
- Front Optics Size: The front lens element of an object-space telecentric lens must be physically larger than the object being measured. Measuring a $200\text{ mm}$ object requires a front lens diameter exceeding $200\text{ mm}$, which can introduce significant weight and cost constraints.
- Alignment Tolerance: Telecentricity relies on precise internal aperture alignment. Drop or impact damage can shift the stop, introducing tilt error and degrading the telecentric behavior.