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# JENar® F-Theta物镜：中功率和大功率应用的激光材料加工

**
JENar™ F-theta物镜可用于各类材料的高精度微构建、打标和贴标。
**

^{™}F-theta物镜特别适用于千瓦范围内的中功率和大功率应用的微加工。您可以在紫外线至可见光和红外线的激光波长下使用标准物镜：您将获得波长为

**1080至266 纳米**的物镜。

业纳的常规F-theta物镜极为耐用，使您能够进行

**高精度激光材料加工**。您可将其用于各类材料的微构建、打标和贴标。物镜配有防护玻璃。作为一项特别服务，我们可以为您提供我们的STEP文件，您可以凭该文件将JENar

^{™}F-theta物镜

**快速**而

**轻松地**集成至任何系统。

每个物镜都经过标准化的应用测试程序。这使得我们能够在批量生产中实现高度一致的光学性能。物镜易于改变且**生命周期稳定性**得以增加，您将因此而受益。

**完整的系统**。对于使用光纤激光器和短脉冲激光器的大功率应用，我们的专家开发了坚固的石英物镜：

**Silverline™ F-theta产品系列**。

## 优势：

**非常耐用：**得益于特殊的低污染安装技术，在认证的洁净室中避免了粘合剂和润滑剂及组装**高精度：**适用于各类材料的微构建、打标和贴标。**灵活：**快速而轻松地集成至现有系统**自定义：**提供标准版或根据个人需求特别定制版产品**高效：**通过对光学组件的热-机械应力的有限元分析，节省资金-
**连续稳定性：**全面的测试保证了现场的可替代性

## 应用领域

**微电子学：**例如，玻璃微结构**半导体工业：**例如，微加工**汽车工业：**例如，切割和构建复合材料**医疗：**例如，在治疗应用中除去纱布-
**一般应用：**例如，玻璃加工，电池焊接

### 产品概况

F-Theta物镜JENar™ | 波长 | 订单编号 | |
---|---|---|---|

03-90FT-125-1030...1080 | 1030...1080纳米 | 017700-003-26 | 数据表 |

03-424FT-350-1030...1080 | 1030...1080纳米 | 017700-009-26 | 数据表 |

100-1030...1080-93 | 1030...1080纳米 | 017700-024-26 | 数据表 |

160-1030...1080-170 | 1030...1080纳米 | 017700-019-26 | 数据表 |

170-1030...1080-170 | 1030...1080纳米 | 017700-018-26 | 数据表 |

255-1030...1080-239 | 1030...1080纳米 | 017700-017-26 | 数据表 |

347-1030...1080-354 | 1030...1080纳米 | 017700-022-26 | 数据表 |

420-1030...1080-420 | 1030...1080纳米 | 017700-021-26 | 数据表 |

03-75FT-100-532 | 515...540纳米 | 017700-202-26 | 数据表 |

03-75FT-108-532 | 515...540纳米 | 017700-203-26 | 数据表 |

100-532-90 | 515...540纳米 | 017700-209-26 | 数据表 |

170-532-160 | 515...540纳米 | 017700-206-26 | 数据表 |

255-532-233 | 515...540纳米 | 017700-205-26 | 数据表 |

330-532-336 | 515...540纳米 | 017700-208-26 | 数据表 |

420-532-420 | 515...540纳米 | 017700-207-26 | 数据表 |

53-355-22 | 355纳米 | 017700-401-26 | 数据表 |

JENar™：在欧盟、中国、日本和新加坡注册的商标|Silverline™：在德国、日本和新加坡注册的商标 F-Theta：在欧盟、中国、韩国、印度和新加坡的注册设计 |

## Downloads

### Basic Principles F theta lenses

#### F-Theta lenses

Jenoptik‘s f theta lenses are optimized for the requirements of laser material processing. 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. If 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 lens translates the constant angular velocity of the polygon to a constant velocity of the spot on the workpiece, thisproblem disappears.

#### Focal length

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.

#### Scan field

When using a galvo 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 galvo 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.

#### Scanner geometry

The geometry of a 2D galvo scanner is very important for the design of an efficient lens. Since the two galvo scan mirrors have to have a certain distance to prevent collision, the application performance will not be rotationally symmetric, instead they will exhibit a two fold 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 in admissable. 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 cannot 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.

#### Telecentricity

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.

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 beamis vanishing, the spot position will not change. This is important 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.

#### Scan angle

The max full diagonal scan angle corresponds to the scanfield diagonal, i.e. using the objective with angles above this maximum angle will lead to clipping of the beam.

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.

#### Input beam diameter

To control stray light, and also reduce the required size of optical elements in laser material processing applications, the incoming Gaussian laser beam will usually be clipped at the diameter where the intensity has fallen to 1/e² of the maximum value. The objectives are designed such that those beams will pass through the objective without being clipped anywhere.

**Application-relevance**

The input beam diameter immediately affects the spot size via the spot size relation anti proportionally. Bigger beam diameters result in smaller spot sizes and vice versa. Using beams with diameters above the maximum allowed beam size will lead to clipping of the beam at the edges of the field.

#### Focus size

When focussing 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 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.

#### Beam-clipping

If the beam diameter of the incoming laser beam is toobig or the scan angle is above the maximum allowedangle, parts of the laser beam might hit mechanical partswhen passing through the objective. This is referred to asclipping of the laser beam.

**Application-relevance**

A laser beam being clipped inside the objective will generateunwanted stray light and might also heat up theobjective leading to thermal focus shift and even destructionof the lens. All JENar Standard and Silverline lensesare designed to show no beam clipping when used withthe scanner setup described on the datasheets.

#### Back working distance

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

**Application-relevance**

The back working distance describes how much freespace there is between workpiece and lens. Sincefocal length and back working distance are closelyrelated, the need for a bigger free space between workpieceand objective usually results in the requirement ofusing lenses with bigger focal lengths.

#### Thermal focus shift

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 as

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/affordable materials is small (fused silica or CaF_{2}) 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. I.e. 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, changesthe 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.

#### Silverline™

Fused silica exhibits extremely small material absorption and is therefore very well suited for being used for high power applications. For their NIR (1064 nm) Silverline™ F-Theta lenses, Jenoptik chooses low-absorbing fused silica material and an optimized lowest-absorbing high performance coating. The maximum absorption of 5 ppm of the coating is guaranteed by a standardized absorption measurement procedure for every coating batch. The manufacturing statistics is shown in the following graph.

**Application-relevance**

(see thermal focus shift)

Therefore, the following absorption values are specified:

NIR SilverlineTM F-theta | Absorption specification |

Material | < 15 ppm/cm |

Coating | < 5 ppm (mean = 3ppm) |

#### Damage threshold LIDT

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 (bigger than 10 ns) the main problem is the accumulation of energy inside the material and subsequent melting and evaporation. For ultra-short pulses (smaller than 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 wave length dependent. Being able to pass more energy per time through anoptical system allows a faster scanning and therefore a higher throughput.

#### Pulse stretching GDD

When light passes through an optical material of non-vanishing dispersion it accumulates a wavelength dependent optical phase. For laser pulses, which are effectively a linear superposition of harmonic oscillations of different wavelengths, this influences the pulse shape.In a second order approximation for gaussian pulses, the temporal stretching of the laser pulse is determined only by the second derivative of the phase change with respect to the light frequency, also called the group delay dispersion (GDD / P2).

The shape of the laser pulse stays gaussian, but its width, expressed as its standard deviation, is scaled as: P3 .

A temporal stretching of the laser pulse reduces its maximal intensity. This might have severe impact on the application performance. To remedy the problem of too long pulses at the workpiece due to pulse stretching one could use lasers with even shorter output pulses. This might increase the intensity above the damage threshold of the involved optical system. Another way would be a precompensation of the induced GDD by gratings, prisms, and microoptial elements (P1).

### 请联系我们的专家，获得相关建议。

### Optics & Optical Systems

+49 3641 65-3677

### Robin Bai

### Light & Optics | North America

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