Gsy chat

Of IncidenceΘ, the angle of incidence, is the angle between the incident beam and the normal to the surface. It is calculated from the triangle P Px R as$$ \Theta = \arccos \frac{d}{{\sqrt { x^{2} + \left( {\sqrt {d^{2} + y^{2} } + e} \right)^{2} } - e/\cos \left( {\theta_{x} } \right)}} $$ (10) Alternatively, it can be expressed as a function of (θx, θy) as$$ \Theta = \arccos \frac{1}{{\left[ {\sqrt {1 + \tan^{2} \left( {\theta_{y} } \right)} + \frac{e}{d}} \right] \cdot \sqrt {1 + \tan^{2} \left( {\theta_{x} } \right)} - \frac{e}{{d \cdot \cos \left( {\theta_{x} } \right) }}}} $$ (11) Equations 9 and 11 shows that Θ changes across the scan area. Θ is also one of the parameters affecting the beam intensity.The OPL is a product of two nonlinear functions that change quickly as the beam moves away from the origin (print center). The OPL is also one of the parameters affecting the beam’s focus and therefore its intensity.SymmetryIt is evident from Eq. 3 that there is symmetry about the origin for GSy, where y(− θy) = − y(θy). Similarly, from Eq. 4, GSx is symmetrical when θy is held constant where x(− θx, θ0) = − x(θx, θ0 ) for θy = θ0. Note also that x is a function of the two inputs θx and θy. However, because the two GSs are positioned at different distances from the work surface (as the distance between GSx and GSy is e), this introduces asymmetry between the two axes.Equations (3) and (4) show that$$ y(\theta_{0} ) \ne x(\theta_{0} )\quad {\text{for}}\quad \theta_{y} = \theta_{x} = \theta_{0} $$Additionally, it is evident from Eqs. 6 and 7 that$$ V_{x} (\theta_{0} ) \ne V_{y} (\theta_{0} )\quad {\text{for}}\quad \theta_{y} = \theta_{x} = \theta_{0} $$This asymmetry and nonlinear speed make it more difficult for the

Possible in relation to d, the distance between GSy and the work surface. The smaller the value of e/d, the smaller the asymmetry around all axes.ModulationModulation in a GS system is performed using a closed loop. The challenges lie in addressing nonlinear transfer functions (position, speed, and energy deposition for printing) and the mechanical inertia of the oscillatory element in the GS. The nonlinear positioning can be addressed by geometric correction techniques.14 Similarly, Zhang15 further measured data spots and performed online calibration of the GS.Duma16 further explored the GS mechanical inertia of the oscillatory element limitation. He qualifies the modulation speed limit to be around 1.5 kHz and selected the preferred/optimized modulation waveform to be a sawtooth wave with fast and slow-moving GS where the raster method is used.Offset/Drift ErrorsOffset/drift errors occur when the GS deviates from the origin and as a result moves all respective coordinates. Offset/drift errors are temperature sensitive and must be watched closely. Offset/drift errors can be addressed by online correction on the fly, in a similar method to Zhang.15Offset errors are measured in microradians. A typical value from a high-quality GS manufacturer is less than 10 microradians. Some manufacturers, unfortunately, amplify the offset/drift error when they make design choices to reduce Θ-related errors. As an example, a company may enlarge d (the distance from the GSy to the work surface) from 500 mm to 2000 mm. Such enlargement of d will reduce the maximum Θ required for the same size work surface, thereby reducing Θ-related errors, but will also amplify offset/drift errors.Consider a 0.1 mm beam diameter using a hash (grid) of 0.1 mm. The position is now dictated by a longer arm d. A typical 5 µrad offset/drift error will result in a 10 µrad error in the correspondent GS θ.If the intended location

Is x0, then the new location is$$ x_{0} \pm {\text{Err}} = x_{0} \pm d \cdot 10\;\upmu {\text{rad}} = x_{0} \pm 20\;\upmu {\text{m}} $$This is already a change of 20% of the grid size. Temperature changes will amplify this error by a factor proportional to the temperature change. As an example, Cambridge Technology for their GS model 83xxK spec reports a zero drift parameter of 5 µrad/°C. A change of 7 °C will thus result in a position change (for d = 2000 mm) of$$ x_{0} \pm {\text{Err}} = x_{0} \pm 5 \cdot 2 \cdot 10^{6} \cdot 7\;\upmu {\text{rad}} = x_{0} \pm 70\;\upmu {\text{m}} $$Note also that this error is only for one GS. Adding the second GS vector will result in a total grid shift of \(\pm {\text{sqrt}}(2) \cdot 70\;\upmu {\text{m}} \to \pm 99\;\upmu {\text{m}}.\)RepeatabilityThe repeatability error is measured in units of microradians. It is doubled when reflecting from the GS mirror. Additionally, the error is further augmented when GSx and GSy errors are combined. A typical value for one GS is 5 µrad to 10 µrad.Energy DensityIn this section, we calculate the volumetric energy density Ev (Eq. 2) as a function of the angle of incidence Θ, taking into account the changes in beam speed and beam diameter discussed above, as well as Lambert’s cosine law.Define OPL’ as the optical path length from the GSy axis to the work surface, where d is the beam distance at focus for a beam converging in Ha. In this way, we can simplify the calculations without using θy or θx:$$ {\text{OPL}}^{\prime } = d/\cos (\Theta ) $$ (18) Ha can be expressed with M the beam size at the mirror and d (Fig. 2):Fig. 2Stage 1 and stage 2 beam enlargementFull size imageSince \({\text{Def}}_{0} \ll M\), we can simplify the term for