We introduce a novel method for correcting distortion in thin silicon substrates caused by coating stress. Thin substrates, such as lightweight mirrors for x-ray or optical imaging, and semiconductor wafers or flat panel substrates, are easily distorted by stress in thin film coatings. We report a new method for correcting stress-induced distortion in flat silicon substrates which utilizes a micro-patterned silicon oxide layer on the back side of the substrate. Due to the excellent lithographic precision of the patterning process, we demonstrate stress compensation control to a precision of ~0.2%. The proposed process is simple and inexpensive due to the relatively large pattern features on the photomask. The correction process has been tested on flat silicon wafers that were distorted by 30 nm-thick compressively-stressed coatings of chromium, achieving RMS surface height and slope error reductions of a factor of 68 and 50, respectively.

The Lynx X-ray Observatory concept, under study for the 2020 NASA Decadal Survey, will require a telescope with ∼2 m 2 of effective area and a point-spread function (PSF) with ∼0.5-arc sec half-power diameter (HPD) to meet its science goals. This requires extremely accurate thin grazing-incidence mirrors with a reflective x-ray coating. A mirror coating, such as 15-nm-thick iridium, can exhibit stress exceeding 1 GPa, significantly deforming segmented mirrors and blurring the PSF. The film stress and thickness are neither perfectly repeatable nor uniform. We use finite element analysis and ray tracing to quantify the effects of integrated stress inaccuracy, nonrepeatability, nonuniformity, and postmounting stress changes on segmented mirrors. We find that if Lynx uses segmented mirrors, it will likely require extremely small film stress (∼10 MPa) and nonuniformity (<1%). We show that realigning mirrors and matching complementary mirror pairs can reduce the HPD from uniform film stress by a factor of 2.3× and 5×, respectively. Doubling mirror thickness produces much less than the 4× HPD reduction that would be expected from a flat mirror. The x-ray astronomy community has developed numerous methods of reducing the PSF blurring from film stress, and Lynx may require several of these in combination to achieve 0.5 arc sec HPD using segmented mirrors.

Fabricating freeform mirrors relies on accurate optical figuring processes capable of arbitrarily modifying low-spatial frequency height without creating higher-spatial frequency errors. We present a scalable process to accurately figure thin mirrors using stress generated by a focused ultrafast laser. We applied ultrafast laser stress figuring (ULSF) to four thin fused silica mirrors to correct them to 10-20 nm RMS over 28 Zernike terms, in 2-3 iterations, without significantly affecting higher-frequency errors. We measured the mirrors over a month and found that dielectric-coated mirrors were stable but stability of aluminum-coated mirrors was inconclusive. The accuracy and throughput for ULSF is on par with existing deterministic figuring processes, yet ULSF doesn’t significantly affect mid-spatial frequency errors, can be applied after mirror coating, and can scale to higher throughput using mature laser processing technologies. ULSF offers new potential to rapidly and accurately shape freeform mirrors.

No abstract

A thermal oxide patterning method has proven to be effective for correcting coating-stress-induced distortion on flat silicon wafers. We report progress on developing this method for correcting curved silicon mirrors distorted by front-side iridium coatings. Owing to the difference in geometry, a finite element model has been established to calculate the appropriate duty cycle maps in thermal oxide hexagon patterns used for compensation. In addition, a photolithographic process, along with three-dimensional printed equipment, has been developed for creating patterns precisely on the back side of curved mirrors. The developed method has been used to recover the original surface shape of two silicon mirrors which are 100-mm long, 0.5-mm thick, having 312-mm radius of curvature, and 30 deg in azimuthal span (Wolter-I geometry). These mirrors' front sides are sputter-coated by 20-nm iridium layers with ∼-70 N∕m integrated stress. Measurement results show that the developed method can mitigate coating-induced distortion by a factor of ∼5 in RMS height and ∼4 in RMS slope error, corresponding to ∼0.5 arc sec RMS slope error. Residual errors after correction are dominated by midfrequency ripples created during the annealing process, which will be resolved in the future. The presented method is precise and inexpensive and a potential candidate for resolving the coating stress issue for Lynx optics in the future.