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Example Systems

Download any of these fully configured optical designs directly into Trefoila, each with surfaces, glass catalog entries, aperture, and field definitions already set up.

Cooke Triplet 2D optical layout
2D Optical Layout
Photographic
Cooke Triplet

The Cooke Triplet is the workhorse of photographic lens design: three elements, two glasses, and a well-corrected image for its simplicity. This f/5 configuration uses N-SK16 crown elements flanking an F2 flint, covering a 40° diagonal field. A good starting point for understanding aberration balancing and glass choice.

Cooke Triplet spot diagram
Spot Grid
Cooke Triplet ray fan
Ray Fan
Cooke Triplet MTF
MTF
Specifications
EFL50 mm
f/#f/5
EPD10 mm
Full field40°
Elements3
GlassesN-SK16 / F2
Wavelengths0.48 – 0.65 µm
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Tessar 2D optical layout
2D Optical Layout
Photographic
Tessar

The Tessar is a four-element design derived from the triplet by splitting the rear element into a cemented doublet, giving a compact, sharp lens with excellent correction across a wide field and the formula behind countless camera lenses from the early 20th century onward.

Tessar spot grid
Spot Grid
Tessar ray fan
Ray Fan
Tessar MTF
MTF
Specifications
EFL52 mm
f/#f/4.5
Full field41°
Elements4
GlassesN-SK15 / F2 / K10
Wavelengths0.48 – 0.65 µm
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Double Gauss 2D optical layout
2D Optical Layout
Photographic
Double Gauss

The Double Gauss is the foundation of most fast normal photographic lenses. Its symmetric arrangement of two Gauss telescope halves produces exceptional correction of coma and lateral colour, making it the go-to starting point for wide-aperture designs. This f/5 example covers a 28° full field at 100mm EFL.

Double Gauss spot grid
Spot Grid
Double Gauss ray fan
Ray Fan
Double Gauss MTF
MTF
Specifications
EFL100 mm
f/#f/5
EPD20 mm
Full field28°
Elements6
Wavelengths0.48 – 0.65 µm
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Petzval 2D optical layout
2D Optical Layout
Portrait / Fast
Petzval

The Petzval lens dates to 1840 and remains one of the fastest corrected designs ever devised. Its characteristic field curvature and swirly off-axis bokeh are prized in portrait photography. This f/1.4 example at 50mm EFL uses N-LAK12 and SF4 to push on-axis performance while retaining the classic character.

Petzval spot grid
Spot Grid
Petzval ray fan
Ray Fan
Petzval MTF
MTF
Specifications
EFL50 mm
f/#f/1.4
Full field14°
Elements4
GlassesN-LAK12 / SF4 / LF5
Wavelengths0.48 – 0.65 µm
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Heliar 2D optical layout
2D Optical Layout
Photographic
Heliar

The Heliar is a five-element symmetric design, essentially a Cooke Triplet with each outer element replaced by a cemented doublet. The additional degrees of freedom allow excellent correction of field curvature and astigmatism across a wide angle. This compact f/5 example has an ~8mm EFL suited to miniature camera formats.

Heliar spot grid
Spot Grid
Heliar ray fan
Ray Fan
Heliar MTF
MTF
Specifications
EFL~8 mm
f/#f/5
Full field20°
Elements5
GlassesN-SK16 / E-LLF6
Wavelengths0.48 – 0.65 µm
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Triplet Telescope 2D optical layout
2D Optical Layout
Telescope / Astrograph
Triplet Telescope

An apochromatic triplet objective optimised for astroimaging. Three elements in air allow independent control of primary and secondary colour, producing a flat, well-corrected field across a 2° full angle at f/2.8. N-BK7 and SF1 are used to balance chromatic aberration without exotic glass.

Triplet Telescope spot grid
Spot Grid
Triplet Telescope ray fan
Ray Fan
Triplet Telescope MTF
MTF
Specifications
EFL100 mm
f/#f/2.8
Full field
Elements3
GlassesN-BK7 / SF1
Wavelengths0.48 – 0.65 µm
Download .trf

Opens directly in Trefoila.
Requires an active license.