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                                                                    EXHIBIT 31.1

                                  CERTIFICATION

I, Robert J. Shillman, President, Chief Executive Officer, and Chairman of the
Board of Directors of Cognex Corporation, certify that:

      1.    I have reviewed this quarterly report on Form 10-Q of Cognex
            Corporation;

      2.    Based on my knowledge, this report does not contain any untrue
            statement of a material fact or omit to state a material fact
            necessary to make the statements made, in light of the circumstances
            under which such statements were made, not misleading with respect
            to the period covered by this report;

      3.    Based on my knowledge, the financial statements, and other financial
            information included in this report, fairly present in all material
            respects the financial condition, results of operations and cash
            flows of the registrant as of, and for, the periods presented in
            this report;

      4.    The registrant's other certifying officer(s) and I are responsible
            for establishing and maintaining disclosure controls and procedures
            (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) for the
            registrant and have:

            (a)   Designed such disclosure controls and procedures, or caused
                  such disclosure controls and procedures to be designed under
                  our supervision, to ensure that material information relating
                  to the registrant, including its consolidated subsidiaries, is
                  made known to us by others within those entities, particularly
                  during the period in which this report is being prepared;

            (b)   [Omitted pursuant to SEC Release Nos. 33-8238 and 34-47986];

            (c)   Evaluated the effectiveness of the registrant's disclosure
                  controls and procedures and presented in this report our
                  conclusions about the effectiveness of the disclosure controls
                  and procedures, as of the end of the period covered by this
                  report based on such evaluation; and

            (d)   Disclosed in this report any change in the registrant's
                  internal control over financial reporting that occurred during
                  the registrant's most recent fiscal quarter (the registrant's
                  fourth fiscal quarter in the case of an annual report) that
                  has materially affected, or is reasonably likely to materially
                  affect, the registrant's internal control over financial
                  reporting; and

      5.    The registrant's other certifying officer(s) and I have disclosed,
            based on our most recent evaluation of internal control over
            financial reporting, to the

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            registrant's auditors and the audit committee of the registrant's
            board of directors (or persons performing the equivalent functions):

            (a)   All significant deficiencies and material weaknesses in the
                  design or operation of internal control over financial
                  reporting which are reasonably likely to adversely affect the
                  registrant's ability to record, process, summarize and report
                  financial information; and

            (b)   Any fraud, whether or not material, that involves management
                  or other employees who have a significant role in the
                  registrant's internal control over financial reporting.

Date: May 10, 2004

                                         /s/ Robert J. Shillman
                                         ----------------------
                                         Robert J. Shillman
                                         President, Chief Executive Officer,
                                         and Chairman of the Board of Directors