{"id":3433,"date":"2021-11-24T15:58:02","date_gmt":"2021-11-24T14:58:02","guid":{"rendered":"https:\/\/lmanew.e6318.servidornet.com\/holografia-electronica\/"},"modified":"2025-01-17T15:18:11","modified_gmt":"2025-01-17T13:18:11","slug":"electron-holography","status":"publish","type":"post","link":"https:\/\/lma.unizar.es\/en\/electron-holography\/","title":{"rendered":"Electron Holography"},"content":{"rendered":"

[et_pb_section fb_built=”1″ _builder_version=”4.14.2″ _module_preset=”default” background_color=”#f2f2f2″ custom_margin=”-1px|||||” custom_padding=”10px||30px|||” box_shadow_style=”preset3″ locked=”off” global_colors_info=”{}”][et_pb_row _builder_version=”4.14.2″ _module_preset=”default” background_color=”#FFFFFF” custom_margin=”12px|auto||auto||” border_width_all=”10px” border_color_all=”#4370b4″ border_style_all=”outset” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.14.2″ _module_preset=”default” global_colors_info=”{}”][et_pb_text _builder_version=”4.14.2″ _module_preset=”default” text_font=”|700||on|||||” text_font_size=”18px” text_orientation=”center” custom_margin=”||13px|||” global_colors_info=”{}”]Transmission electron microscopy (TEM) area[\/et_pb_text][et_pb_button button_url=”https:\/\/lma.unizar.es\/en\/transmission-electron-microscopy-tem-area\/” button_text=”SEE EQUIPMENT” button_alignment=”center” _builder_version=”4.14.2″ _module_preset=”default” custom_button=”on” button_text_size=”16px” button_bg_color=”#FFFFFF” button_border_width=”0px” button_border_radius=”4px” button_letter_spacing=”0px” button_font=”|700||on|||||” button_icon=”=||divi||400″ custom_margin=”0px||8px||false|false” custom_padding=”4px||4px||true|false” hover_enabled=”0″ button_text_color_tablet=”” button_text_color_phone=”” button_text_color_last_edited=”on|desktop” global_colors_info=”{}” button_bg_color__hover=”#4370b4″ button_bg_color__hover_enabled=”on|hover” button_text_color__hover=”#FFFFFF” button_text_color__hover_enabled=”on|hover” button_border_color__hover=”#4370b4″ button_border_color__hover_enabled=”on|desktop” sticky_enabled=”0″][\/et_pb_button][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”4.9.4″ _module_preset=”default” custom_padding=”21px||16px|||” global_colors_info=”{}”][et_pb_row _builder_version=”4.9.4″ _module_preset=”default” max_width=”75%” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.4″ _module_preset=”default” global_colors_info=”{}”][et_pb_text _builder_version=”4.9.4″ _module_preset=”default” text_line_height=”2em” header_2_font=”|700|||||||” header_2_font_size=”18px” header_2_line_height=”1.8em” global_colors_info=”{}”]<\/p>\n

Electron Holography form quantitative magnetic fields mapping<\/h2>\n

Off-axis Electron Holography (EH) is an interferometric technique that allows the measurement of the phase shift of the electron wave having interacted with static electrostatic and magnetic fields. This phase shift gives quantitative information about these electromagnetic fields.<\/p>\n

In off-axis EH the phase shift measurement is performed by overlapping a so-called \u201creference\u201d beam, which has not interacted with any field and just travelled through the vacuum, and a beam that has been phase shifted after interaction with any electromagnetic field inside the sample and with possible stray fields out of it. The overlapping of the two beams is realized thanks to an electrostatic biprism (M\u00f6llenstedt biprism) located in the SA image plane. This produces an interference pattern (a hologram) which can be analyzed quantitatively to determine the phase shift.[\/et_pb_text][et_pb_image src=”https:\/\/lma.unizar.es\/wp-content\/uploads\/2021\/11\/holografia-electronica-1.jpg” title_text=”holografia-electronica-1″ align=”center” _builder_version=”4.9.4″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.9.4″ _module_preset=”default” text_line_height=”2em” header_2_font=”|700|||||||” header_2_font_size=”18px” header_2_line_height=”1.8em” global_colors_info=”{}”]<\/p>\n

overlap creates an interference pattern (i.e. the hologram) between the two beams:<\/span><\/p>\n

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where <\/span>\u03c8<\/span>ref<\/span> is the reference electron wave; <\/span>\u03c8<\/span>s<\/span> the electron wave that has been phase shifted, A<\/span>s<\/span> the amplitude of <\/span>\u03c8<\/span>s<\/span>, <\/span>\u03c6<\/span>s<\/span>(x,y) its phase shift after interaction with the sample and surrounding stray fields, R<\/span>O<\/span> the periodicity of the hologram fringes (which depend on the polarization of the biprism and the accelerating voltage).<\/span><\/p>\n

The phase shift <\/span>\u03c6<\/span>s<\/span>(x,y) is given by the Aharonov-Bohm effect:<\/span><\/p>\n

[\/et_pb_text][et_pb_image src=”https:\/\/lma.unizar.es\/wp-content\/uploads\/2021\/11\/holografia-electronica-3.jpg” title_text=”holografia-electronica-3″ align=”center” _builder_version=”4.9.4″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.9.4″ _module_preset=”default” text_line_height=”2em” header_2_font=”|700|||||||” header_2_font_size=”18px” header_2_line_height=”1.8em” global_colors_info=”{}”]<\/p>\n

where V(x,y,z) is the electrostatic potential, B<\/span>(x,y,z)\u00a0 the component of the magnetic induction perpendicular to the beam ; C<\/span>E<\/span>\u00a0a constant depending on the beam energy, and e and <\/span>\u210f<\/span> the electron charge and Planck constant, respectively.<\/span><\/p>\n

The phase shift then contains two terms:<\/span><\/p>\n