F-Theta lenses made for laser material processing

Jenoptik‘s F-Theta objectives are optimized for the requirements of laser material processing. They realize even focal planes over the scan area independent from scan angle. On the one hand, they are designed to yield excellent optical performance, manifesting itself in small field curvature, small distortion and diffraction limited focus sizes. On the other hand, F-Theta lenses realize a linear dependence between the angle Θ of the incoming laser beam and the image height h of the focussed spot on the workpiece. The proportionality factor is the focal length f. This relation is mathematically expressed as h = f Θ, which gives those special lenses their name "F-Theta."

Application relevance

Whereas the merits of good optical performance are easy to see, the advantages of the F-Theta relation are more subtle and best understood considering polygon scanners. Those scanners rotate with a constant angular velocity at very high scan speeds for dynamic processing. If, for example, the image height would be proportional to the tangens of Θ, then the speed of the spot on the workpiece would increase for higher angles, and therefore, the energy deposited in the material would decrease, possibly resulting in inhomogeneous application performance. Since the F-Theta objective translates the constant angular velocity of the polygon to a constant velocity of the spot on the workpiece, this problem disappears. F-Theta lenses can be used for high speed processing with very reliable quality. This allows for most efficient laser material processing.

In theoretical nomenclature, the focal length is the distance from the second cardinal plane to the paraxial focus point of the objective. That means, if one would represent the objective as having vanishing length, then the distance from this ideal lens to the focus would be the focal length.

Application relevance

From the F-Theta relation h = f * theta, the image height is proportional to the focal length, i.e. if one wants to increase the area of application then one can use lenses with bigger focal length. However, if one wants to retain the same spot size, then, according to the focus size definition, one would also have to increase the laser input beam size. Another property is the distance between lens and workpiece. If this has to be increased, usually an increase in focal length is required (see also back working distance).

In theoretical nomenclature, the focal length is the distance from the second cardinal The max full diagonal scan angle corresponds to the scan field diagonal, i.e. using the objective with angles above this maximum angle will lead to clipping of the beam.

Application relevance

From the F-Theta relation one sees that an increase of the field size can also be achieved by using bigger scan angles. This would have the advantage that the beam size would stay the same. However, big scan angles pose a considerable complication for the design of cost effective F-Theta lenses.

When focusing light, the spot size σ can not surpass the limit of diffraction, i.e. the spot size does not depend on the aberrations of the lens anymore but only on the physical properties wavelength λ, the input beam diameter Ø, and the focal length f. As for the laser input beam diameter, it is common to define the focus size as the diameter at which the intensity is dropped to 1/e² of the maximum intensity at the spot center. For input beams defined as in "input beam diameter," the focus size is given as σ = 1.83 λ f / Ø.

Application relevance

Decreasing the focus size immediately decreases e.g. the structure sizes of the patterns written. It also increases the maximum intensity in the center of the spot, therefore lifting it above the application threshold of a particular material. If, however, the intensity is way above the application threshold, the energy not needed for the application processed is deposited in the material leading to varying non-controllable side effects, possibly reducing the application performance. Therefore, the user has to find the optimal focus size for the application under question.

If the beam diameter of the incoming laser beam is too big or the scan angle is above the maximum allowed angle, parts of the laser beam might hit mechanical parts when passing through the objective. This is referred to as clipping of the laser beam.

Application relevance

A laser beam being clipped inside the objective will generate unwanted stray light and might also heat up the objective leading to thermal focus shift and even destruction of the lens. All JENar™ Standard and Silverline™ lenses are designed to show no beam clipping when used with the scanner setup described on the datasheets.

Whereas the focal length is a rather theoretical construct, the back working distance describes the real distance between the end of the objective (the edge closest to the workpiece) and the workpiece.

Application relevance

The back working distance describes how much free space there is between workpiece and lens. Since focal length and back working distance are closely related, the need for a bigger free space between workpiece and objective usually results in the requirement of using lenses with bigger focal lengths.

When using a galvanometric 2D-scanner, changing the mirror angles moves the laser spot over the workpiece. The Jenoptik‘s F-Theta lenses are then optimized for a quadratic scan field where the diagonal of this square is denoted as the scan field diagonal.

Application relevance

If the galvanometer mirrors are tilted more than the angles corresponding to the quadratic scan field area two major effects appear. Firstly, the optical performance will degrade above diffraction limit, and secondly the laser beam might be clipped inside the objective (see beam-clipping).

Telecentricity describes the angle of the centroid of the laser beam at the edge of the scan field, for example how much the entire beam is tilted with respect to the optical axis.

Application relevance

Telecentric lenses usually show a more homogeneous focus size distribution over the full field. Furthermore, telecentric lenses are more "scale preserving“ when the workpiece is defocussed. For example, if the workpiece is moved away from the lens, but the tilt of the laser beam is vanishing, the spot position will not change. This is important for example in drilling applications. An immediate consequence of a small telecentricity angle is that the lenses have approximately the same diameter as the field diagonal. Therefore, telecentric lenses are usually more expensive than non-telecentric ones.

The geometry of a 2D galvanometric scanner is very important for the design of an efficient lens. Since the two scan mirrors must have a certain distance to prevent collision, the application performance will not be rotationally symmetric, instead they will exhibit a twofold mirror-symmetry in X and Y. The distance between the mirrors is given by the parameter a1. The distance from the second mirror to the flange of the objective is described by parameter a2. The separation of mirrors makes the physical concept of a pupil inadmissable. One therefore defines an effective pupil as being positioned in the middle between the two mirrors. The non-existence of a real pupil also has the consequence that a 2D-galvanometric scan system can not be perfectly telecentric.

Application relevance

Different optical properties of an existing F-Theta lens can be modified by modifying the scanner geometry. But care must be taken not to create clipping of the laser beam somewhere in the objective. For example, increasing the distance between objective and effective pupil changes the telecentricity angle (usually it decreases it). But to prevent clipping the maximum scan angle, and therefore the maximum field size, must be reduced as well.

The laser induced damage threshold (LIDT) describes the laser intensity (or fluence) above which damage of the lenses occurs. This threshold depends on several parameters like wavelength and pulse duration and involves different physical phenomena. For CW and long pulses (> 10 ns) the main problem is the accumulation of energy inside the material and subsequent melting and evaporation. For ultrashort pulses (< 10 ps), on the other hand, non-thermal processes like avalanche ionization and coulomb explosion are dominant reasons for damage. This variety of different processes makes an analytical description very difficult and for industrial purposes it seems to be advisable to test coatings and materials and derive phenomenological descriptions.

Jenoptik tested its standard coatings and materials for the most common application parameters and expressed the pulse-duration dependent damage threshold fluence Φ in terms of a power law of the pulse duration τ. Φ = c * τ ^ p The parameters c and p of this law are wavelength-dependent. Furthermore, the real damage threshold of the system critically depends on several exterior influences, like adequate storage, handling, and cleaning. Inappropriate care of the optical systems reduces the damage threshold and renders the guarantee obsolete. Due to varying intensities inside of the optical system, the system damage threshold might vary from the single element coating damage threshold.

Application relevance

The ability to pass more energy per time through an optical system allows a faster scanning and therefore a higher throughput.

In spite of anti-reflective coatings at highest quality on our optical components low residual reflection can occur and cause beam paths that can get focussed on other optical components. By this and depending on the laser power the affected component can change its characteristics or – in case of extreme illumination – can be damaged.

Hence, Jenoptik particularly considers these effects during the design phase of F-Theta-lenses and beam expanders. The optical design is optimized to place focal planes of reflected beam paths outside optical components and scanners.

In case of different optical setups, e.g.

• Including additional cover glasses
• Differing cover glass mounting
• Divergent or convergent beam paths
• Use of lenses with other scanning systems
  
• Differing distances between scanning system and lenses
• Reflexes by work pieces (e.g. glasses without anti-reflective coating) back reflection positions can change and can cause damage on optical components or scanning mirrors.

To prevent these effects and ensure reliable operating conditions we would like to ask you to contact us to tune your system.

When the temperature of an optical material changes, the corresponding shape and index of refraction change. These two effects alter the optical properties of the system, mainly the focus position. This change in position is called the thermal focus shift. An objective can be optimized to withstand a global homogeneous temperature change (due to variations of room temperature and sufficient time of relaxation), for example by employing temperature dependent spacers. However, when used with a high power laser, the temperature distribution over the lens elements becomes non-homogeneous and also scan-pattern dependent. The only way to make objectives insensitive towards these effects is to reduce the change in temperature, for example reduce absorption in lens and coating material.

The induced thermal focus shifts for top-hat (Δz_T) and Gaussian (Δz_G) intensity distributions can be calculated analytically. P_0 is the input power of the laser. f is the focal length of the lens. The sum is then over all optical elements in the system, indicated by the index i. n_i and dn/dT_i describe the index of refraction and its thermal derivative. alpha_i is the thermal expansion coefficient, lambda_i is the heat conduction coefficient, A_i and B_i describe the absorption coefficients of coating and material respectively. d_i is the thickness of the element, and phi_i is the diameter of the laser beam on element i.

For high power applications, the range of usable materials is small (fused silica or CaF2) which fixes most of the material coefficients (dn/dT, n, alpha, lambda). Furthermore, the application requirements determine the parameters input power (P_0) and focal length (f) and the beam sizes (phi) on and thickness (d) of the elements in an F-Theta lens usually constitute no powerful optimization parameters. In essence, optical designs which fulfill the optical specification usually do not differ very much in their respective lens shapes. Therefore, the most promising strategy to reduce the thermal focus shift of a system is to reduce the amount of energy being absorbed. This can be achieved by choosing low absorbing materials and coatings.

Application relevance

A thermal focus shift, when uncompensated, changes the application performance over time. A workpiece being in perfect focus at the beginning of the process might be considerably out of focus after some process-time and the application result will look very different.