This thesis investigates self-aligned focusing schlieren (SAFS) as a step toward future volumetric and quantitative measurements of three-dimensional compressible flows. Conventional schlieren imaging provides valuable visualization of density gradients, but it records only a line-of-sight projection and therefore does not directly resolve the spatial distribution of structures through the depth of the flowfield. SAFS addresses part of this limitation by introducing depth sensitivity, but its depth response has not been well characterized quantitatively. To help lay the foundation for future volumetric and quantitative SAFS methods, this work addresses two related problems. First, calibrated quantitative schlieren imaging is applied to an overexpanded supersonic jet to demonstrate how schlieren image intensity can be related to ray displacement, angular deflection, refractive index gradient, and density. The reconstructed mean density fields capture the expected shock-cell structure and agree well with the corresponding mean schlieren images, showing that physically meaningful density information can be recovered from schlieren data. Second, the depth response of a SAFS system is characterized experimentally using a Fourier optics framework based on the modulation transfer function (MTF) and point spread function (PSF). Depth-dependent MTF measurements from a slanted-edge target and PSF measurements from a 100 µm pinhole target show that the depth response of the SAFS system changes gradually with defocus, depends strongly on direction, and is influenced by diffraction from the Ronchi ruling in addition to defocus blur. Comparison with conventional depth-of-field definitions shows that no single geometric limit fully describes the measured behavior, although depth of sharp focus provides the closest agreement. Taken together, these results establish the groundwork for extending SAFS beyond qualitative visualization and toward future methods for resolving and quantifying three-dimensional density gradient structures found in compressible flows.
","abstract_html":"<p>This thesis investigates self-aligned focusing schlieren (SAFS) as a step toward future volumetric and quantitative measurements of three-dimensional compressible flows. Conventional schlieren imaging provides valuable visualization of density gradients, but it records only a line-of-sight projection and therefore does not directly resolve the spatial distribution of structures through the depth of the flowfield. SAFS addresses part of this limitation by introducing depth sensitivity, but its depth response has not been well characterized quantitatively. To help lay the foundation for future volumetric and quantitative SAFS methods, this work addresses two related problems. First, calibrated quantitative schlieren imaging is applied to an overexpanded supersonic jet to demonstrate how schlieren image intensity can be related to ray displacement, angular deflection, refractive index gradient, and density. The reconstructed mean density fields capture the expected shock-cell structure and agree well with the corresponding mean schlieren images, showing that physically meaningful density information can be recovered from schlieren data. Second, the depth response of a SAFS system is characterized experimentally using a Fourier optics framework based on the modulation transfer function (MTF) and point spread function (PSF). Depth-dependent MTF measurements from a slanted-edge target and PSF measurements from a 100 µm pinhole target show that the depth response of the SAFS system changes gradually with defocus, depends strongly on direction, and is influenced by diffraction from the Ronchi ruling in addition to defocus blur. Comparison with conventional depth-of-field definitions shows that no single geometric limit fully describes the measured behavior, although depth of sharp focus provides the closest agreement. Taken together, these results establish the groundwork for extending SAFS beyond qualitative visualization and toward future methods for resolving and quantifying three-dimensional density gradient structures found in compressible flows.</p>","abstract_has_math":false,"creators":["Ephraim, Alexander"],"institution":null,"degree_name":"Master of Science in Aerospace Engineering","degree_level":"Thesis - Open Access","degree_discipline":"Aerospace Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026-04-01T07:00:00Z","date_published":"2026-04-01T07:00:00Z","updated_at":"2026-07-27T19:26:22Z","subjects":["Self-aligned Focusing Schlieren","Schlieren Imaging","Fourier optics","modulation transfer function","point spread function","depth of field","density-field reconstruction","compressible flow","Aerodynamics and Fluid Mechanics","Other Engineering"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.erau.edu/edt/983","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Ephraim, Alexander"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Aerospace Engineering"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Self-aligned Focusing Schlieren","Schlieren Imaging","Fourier optics","modulation transfer function","point spread function","depth of field","density-field reconstruction","compressible flow","Aerodynamics and Fluid Mechanics","Other Engineering"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.erau.edu/edt/983"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis investigates self-aligned focusing schlieren (SAFS) as a step toward future volumetric and quantitative measurements of three-dimensional compressible flows. Conventional schlieren imaging provides valuable visualization of density gradients, but it records only a line-of-sight projection and therefore does not directly resolve the spatial distribution of structures through the depth of the flowfield. SAFS addresses part of this limitation by introducing depth sensitivity, but its depth response has not been well characterized quantitatively. To help lay the foundation for future volumetric and quantitative SAFS methods, this work addresses two related problems. First, calibrated quantitative schlieren imaging is applied to an overexpanded supersonic jet to demonstrate how schlieren image intensity can be related to ray displacement, angular deflection, refractive index gradient, and density. The reconstructed mean density fields capture the expected shock-cell structure and agree well with the corresponding mean schlieren images, showing that physically meaningful density information can be recovered from schlieren data. Second, the depth response of a SAFS system is characterized experimentally using a Fourier optics framework based on the modulation transfer function (MTF) and point spread function (PSF). Depth-dependent MTF measurements from a slanted-edge target and PSF measurements from a 100 µm pinhole target show that the depth response of the SAFS system changes gradually with defocus, depends strongly on direction, and is influenced by diffraction from the Ronchi ruling in addition to defocus blur. Comparison with conventional depth-of-field definitions shows that no single geometric limit fully describes the measured behavior, although depth of sharp focus provides the closest agreement. Taken together, these results establish the groundwork for extending SAFS beyond qualitative visualization and toward future methods for resolving and quantifying three-dimensional density gradient structures found in compressible flows.
"]},{"key":"dc:title","label":"Title","values":["Quantification of the Depth-of-Field in a Self-Aligned Focusing Schlieren System"]}]}],"canonical_facts":{"dc:creator":["Ephraim, Alexander"],"dc:description.abstract":["This thesis investigates self-aligned focusing schlieren (SAFS) as a step toward future volumetric and quantitative measurements of three-dimensional compressible flows. Conventional schlieren imaging provides valuable visualization of density gradients, but it records only a line-of-sight projection and therefore does not directly resolve the spatial distribution of structures through the depth of the flowfield. SAFS addresses part of this limitation by introducing depth sensitivity, but its depth response has not been well characterized quantitatively. To help lay the foundation for future volumetric and quantitative SAFS methods, this work addresses two related problems. First, calibrated quantitative schlieren imaging is applied to an overexpanded supersonic jet to demonstrate how schlieren image intensity can be related to ray displacement, angular deflection, refractive index gradient, and density. The reconstructed mean density fields capture the expected shock-cell structure and agree well with the corresponding mean schlieren images, showing that physically meaningful density information can be recovered from schlieren data. Second, the depth response of a SAFS system is characterized experimentally using a Fourier optics framework based on the modulation transfer function (MTF) and point spread function (PSF). Depth-dependent MTF measurements from a slanted-edge target and PSF measurements from a 100 µm pinhole target show that the depth response of the SAFS system changes gradually with defocus, depends strongly on direction, and is influenced by diffraction from the Ronchi ruling in addition to defocus blur. Comparison with conventional depth-of-field definitions shows that no single geometric limit fully describes the measured behavior, although depth of sharp focus provides the closest agreement. Taken together, these results establish the groundwork for extending SAFS beyond qualitative visualization and toward future methods for resolving and quantifying three-dimensional density gradient structures found in compressible flows.
"],"dc:identifier":["https://commons.erau.edu/edt/983"],"dc:subject":["Self-aligned Focusing Schlieren","Schlieren Imaging","Fourier optics","modulation transfer function","point spread function","depth of field","density-field reconstruction","compressible flow","Aerodynamics and Fluid Mechanics","Other Engineering"],"dc:title":["Quantification of the Depth-of-Field in a Self-Aligned Focusing Schlieren System"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["Thesis - Open Access"],"thesis:degree_name":["Master of Science in Aerospace Engineering"]},"updated_at":"2026-07-27T19:26:22Z"}