considering they are searching for one specific image
That was not the case. They were authorized by warrant to search for the following, which I transcribed from a copy of the affidavit in support of application for warrant:
A. Personal computer hardware to include, the computer system case with internal components, motherboard, CPU, memory, etc., internal and peripheral storage devices (such as fixed disks, external hard disks, floppy disk drives and diskettes, tape drives and tapes, zip drives, optical storage devices, transistor-like binary devices, video cameras, digital cameras, cell phones, and any other memory storage devices); peripheral input/output devices (such as keyboards, mouse/track ball/pad, video display monitor); and all related cables, power cords and connections, RAM or ROM units or CD ROM; as well as any devices, mechanisms, or parts that cat be used to restrict access to computer hardware (such as physical keys and locks).
B. Computer software applications used by the computer system and any related components.
C. Computer-related documentation that explains or illustrates how to configure or use the computer hardware, software, or other related items/devices. The documentation consists of written, recorded, printed, or electronically stored material.
D. Computer-related passwords and other data security devices designed to restrict access or hide computer software, documentation, or data.
E. Digital data that may be kept on any computer related storage device listed in 'A' above. The specific data will be (or will contain or incorporate) digital video and/or image files depicting minors engaged in sexually explicit conduct, any digital data related to the trading or exchange of depictions of minors engaged in sexually explicit conduct, and any digital "user attribution" evidence to include, but not limited to, registry information, configuration files, user profiles, e-mail, e-mail address books, "chat," instant messaging logs, photographs, and correspondence (and the data associated with the foregoing, such as file creation and last accessed dates) that may be evidence of who used or controlled hte computer or storage medium at a relevant time.
F. Photographs of the interior and exterior of the listed residence.
G. Papers showing dominion and control.
H. Any other evidence of the crimes of RCW 9.68A.070, to include but not limited to videotapes, books, magazines, catalogs, photographs, film, diaries, or other documents pertaining to the possession or dealing of child pornography, to include printed material documenting any communication with other persons regarding the trading or exchange of depictions of minors engaged in sexually explicit conduct.