ƒ-theta lenses


General explanations

Lenses used in combination with XY galvanometer scanners or polygon scanners are so-called ƒ-theta lenses, plane field objectives or scan lenses.


Our ƒ-theta lenses are used in various applications from industrial material processing (e.g. drilling, welding of synthetic materials or cutting) in addition to medical and biotechnological applications (confocal microscopy, ophthalmology) and science and research. The design and the quality of the optical components play a key role in the lens performance.


Standard lenses focus the laser beam on a spherical surface in contrast to an ideal flat or plane field. The use of ƒ-theta lenses provides a plane focusing surface and almost constant spot size over the entire XY image plane or scan field. The position of the spot on the image plane is directly proportional to the scan angle.


The scan length or scan area specifications in this catalog are based on mirror spacing of typical scan heads. For other scan systems the parameter “aperture stop” defines the distance of the geometrical center between the mirrors to the mechanical edge of the lens housing. The calculated values take a maximum vignetting of 1 % into account.


Lenses which are marked with the following sign are manufactured only on request.

Lens type recommendation

As previous explanations about LIDT demonstrated, the correct selection of a lens to the laser used and process requirements can be difficult and a general statement about usability is not possible. Therefore some basic lens properties are explained here, which are typically needed for specific laser types and give a rough guideline for any selection process.

Internal ghosts

Ghosts or back reflections occur as a portion of laser light is reflected from a lens or protective window surface to a previous lens element.


Laser lenses are coated with anti-reflective coatings which transitions the light from the index of refraction of air to the refractive index of the bulk material of the lens. This reduces the back reflections of each surface from 4 % to 0.2 %. In spite of low-absorption losses a usage of lenses with internal ghosts and SP and USP lasers often results in exceeding the damage threshold of the coating or bulk material.


Most scan lenses have anywhere from two to six lens elements. The solution is a special design which prohibits internal ghosts nearby any lens element. We strongly recommend the use of such “ghost free” lenses in combination with high and mid power lasers (up in the kilowatt-range) as well as with short pulsed lasers. USP usable and ghost free lenses are marked with a •. They consist of glasses with a low temperature coefficient (e.g. fused silica) without any cemented surfaces.

External ghosts

Ghosts are back reflections from lens surfaces or from the protective window. High power lasers are able to damage optical elements which are positioned nearby the back reflection.


On the one hand the focus of an internal ghost is positioned on top of a glass surface inside the lens. Lenses with internal ghosts are generally not suitable for high power lasers.


On the other hand there are external ghosts whose foci are positioned outside of the housing. High power lasers can be used safely in this case. But it is important to choice the distance between lens and the rest of the optical setup advisedly. If the external ghost is on top of an optical element (normally scanner mirror) a damage be generated there.


On the datasheet there is a field called “back reflection position” which specifies all external ghost positions. The distance is measured between the focal point on the optical axis and the frame border. The middle chief ray is the basic for the simulation. Tilting the beam results in a position change of the external ghost. Because of that optical elements in front of the lens should not be positioned nearby the ghost position (minimum safety distance to the ghost position = a few millimeters (half scanner aperture)).

Fused silica glass with low-absorption coating

Fused silica is a very resistive glass type which has also a very low thermal expansion coefficient compared to other optical glasses. Therefore it is commonly used to minimize thermal effects. Sill Optics also uses a special low-absorption coatings with all fused silica objectives to minimize thermal effects further and increase typical damage thresholds. Fused silica combined with low-absorption coatings are recommended for the use with all high power or short-pulse lasers.

Spot expansion for applications with USP lasers

Im Jahr 1927 formulierte Werner Heisenberg seine Unschärferelation, die besagt, dass zwei komplementäre Eigenschaften eines Teilchens nicht gleichzeitig beliebig genau bestimmbar sind. Dieses Phänomen führt bei modernen ultrakurz gepulsten Lasern zu Problemen. Insbesondere bei sehr geringen Pulsdauern im Bereich von einigen hundert Femtosekunden kann die Wellenlänge der emittierten Photonen nicht mehr genau bestimmt werden. Die bei langen Pulsen klar definierbare Wellenlänge verschwimmt somit bei UKP-Lasern und führt zu einer Erhöhung von deren Bandbreite. Dabei hängt die Intensität der spektralen Verbreiterung von der Sollwellenlänge sowie der Pulsdauer ab. Je kürzer der Puls und je größer die Wellenlänge, desto breiter ist der Unschärfebereich.

Therefore, a non-color-corrected scan lens produces a highly extended spot in broadband USP laser applications. Special color-corrected lenses can solve this problem, but they are often very expensive because of the limited choice of glass material. Highly absorbing optical glasses are not suitable for USP applications and would quickly heat up and cause permanent damages inside the lens.

Although the bandwidth of UKP lasers is usually smaller in the ultraviolet range, the color is difficult to correct especially for short wavelengths. While the spot is sometimes still applications with non-color-corrected objectives, its shape in the UV range very often deviates strongly from the nominal. The achieved Gaussian shape turns into an elliptical or even linear shape. The longitudinal distortion of the spot is caused by many spectral components that are focused with an offset on the working plane. The offset is much larger for strongly tilted ingoing beams than in the more central areas.

Sill Optics offers three different USP-usable color-corrected scan lenses in its catalog and is always ready to develop customer-specific acceptable in short-pulsed long-wavelength lenses with new focal lengths.

Optical and mechanical scan angle

The optical scan angle describes the maximum angle of the beam into the entrance aperture of the scan lens to avoid vignetting. Be aware that the max. mechanical scan angle, which describes the angle of the scan mirrors, is half the value of the optical scan angle.

Aperture stop and scan mirror distances

F-theta lenses are designed to focus a laser beam onto a planar image plane. They are often used in a scanning system with two galvanometer mirrors. One mirror is responsible for beam deflection in one direction and the second one for the perpendicular direction. For simulation purposes an aperture stop is placed exactly in the middle between both mirrors. In real applications, there is no mechanical border to create any kind of aperture stop there. The following sketch shows an illustration of the optical elements involved on the optical axis.

Change of the scan position

You can find recommended lens and mirror positions at the outline and specification table from the datasheet. Using the same distances would be the best option. But there are some applications without any possibility for these positions because of different scanner models, less installation space or scanner mirrors which cannot be tilted enough. If there is a change of the scan lens position specification changes will result.

If the user increases the distance between ƒ-theta lens and scanner the scan field will reduce because of the increasing beam height at the lens. Vignetting of the outer beams reduces the maximum scan field.

Furthermore the telecentricity error may increase if the aperture stop distance changes. The aperture stop distance on top of the datasheet is the best distance for a minimum telecentricity error.

The recommended mirror distances are typical mirror distances for some known scanner models. If you use the recommended mirror distances there are no back reflections at or nearby the scanner mirrors. If you change the position of the scan field it is very important to check the back reflection positions to ensure that there are also no external ghosts nearby the mirror positions, which can damage these surfaces.

If it is necessary to use a not recommended scan lens position please feel free to ask our technical team for specification changes and the back reflection positions. Please inform them about your mirror positions and the

Spot diameter diagram

The spot diameter diagram is a color diagram which indicates the spot diameter variation depending on its field position. The color gradient ranges from the smallest value in white to the largest value in blue. Both axis cover the max. scan field. The scales on the axes show the position in the working area [mm] with the middle placed point of origin. At the lower and upper end of the axes you can see the minimum / maximum field position and the mechanical mirror tilt [°].


The size of the beam diameter depends on the laser beam quality factor M² and the entrance beam diameter. Sill assumes M² to be equal to one, thus a rough estimation is done by multiplication of the actual M² of the laser. The spot diameter is the diameter of the circle which includes 86.5 % (1/e²) of the impacting laser power.


The spot diameter diagram is not always referred to the maximum clear aperture. In some applications beam intensities are so high, that vignetting at the 1/e² value would be unacceptable. Details about the input beam diameter used in simulation are given in the text below the diagram.


Most designs are diffraction limited on the entire scan field. But even these lenses show a varying spot size, because the diffraction limit changes over the scan field. The percentage value on top of the color scale specifies the intensity of this variation.


Example: Spot diameter diagram of S4LFT4010/292 ƒ-theta lens


A scan lens is telecentric if all beams (at the field center and edges) meet the working plane in a vertical way. The telecntricity error is the maximum angle between the focused beam and the perpendicular of the working plane. Normally this value is larger at the scan field edges.

Perfect telecentricity is only possible if all light comes from one plane. If the distance between this plane and the first surface of the lens housing is the same as the back focal length the scan lens is telecentric.

Galvanometer scanner tilt the beam in x- and y-direction by using two neighbored mirrors. A beam displacement which depends on the mirror tilt results. For reaching the best telecentricity it is necessary to place the theoretical plane all beams should come from (= back focal length) exactly in the middle of the two scanner mirrors. If this plane is no longer placed between the two scanner mirrors the lens is not telecentric.

Black Box files for Zemax OpticStudio®

Standard Sill lenses are calculated for a certain scan head, but it is also possible to use them in combination with other scanners. A variation of the mirror distances or of the input beam diameter influences specifications like e.g. scan field size, spot diameter or telecentricity error. Black Box files can be helpful for simulating specifications of a complete system within a custom specific environment. This applies not only to ƒ-theta lenses but also to lens systems which should be integrated into an optical setup. These files show the performance of a lens without disclosing its design.


For opening you have to save the file in the folder “Zemax” → ”Black Box” so that the program has access to the data. After that you can insert a new surface into your design file and set “Surface Type” to “Black Box Lens”. In order to insert the Black Box put the full name of the Black Box file into the field “comment” (e.g. “f-theta-lens.ZBB”). In principle it is possible to get a Black Box file of any Sill lens on request.