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                                                                     EXHIBIT 4.1

                       AMENDMENT NO. 2 TO RIGHTS AGREEMENT

                  This AMENDMENT NO. 2 (this "Amendment No. 2") is being entered
into as of July 11, 2002, between Veeco Instruments Inc., a Delaware corporation
(the "Company"), and American Stock Transfer and Trust Company, a New York
banking corporation, as rights agent (the "Rights Agent").

                  WHEREAS, the Company and the Rights Agent are parties to a
Rights Agreement, dated as of March 13, 2001, between the Company and the Rights
Agent, as previously amended pursuant to the Amendment to Rights Agreement dated
as of September 6, 2001 (the "Rights Agreement");

                  WHEREAS, simultaneously with the execution of this Amendment
No. 2, the Company is entering into an Agreement and Plan of Merger (the "FEI
Merger Agreement") by and among the Company, Venice Acquisition Corp., an Oregon
corporation and a wholly-owned subsidiary of the Company ("Acquisition") and FEI
Company, an Oregon corporation ("FEI"), pursuant to which Acquisition will merge
with and into FEI with the result that FEI will be the surviving corporation and
shall become a wholly-owned subsidiary of the Company (the "FEI Merger");

                  WHEREAS, pursuant to the FEI Merger, Philips Business
Electronics International B.V. ("Philips"), a significant stockholder of FEI,
will receive approximately 11,198,832 shares of common stock and other
securities of the Company, representing approximately 15% of the shares of
common stock of the Company expected to be outstanding as of the Effective Time
(as defined in the FEI Merger Agreement);

                  WHEREAS, simultaneously with the execution of this Amendment
No. 2, the Company is entering into that certain Investor Agreement dated the
date hereof between the Company, Philips and FEI; and

                  WHEREAS, pursuant to Section 27 of the Rights Agreement, the
Company and the Rights Agent may supplement or amend the Rights Agreement in
accordance with the provisions of Section 27 thereof. The Company now desires to
amend the Rights Agreement as set forth in this Amendment No. 2 and deems such
amendments to be necessary and desirable. Capitalized terms used but not defined
herein shall have the meanings ascribed to such terms in the Rights Agreement.

                  NOW THEREFORE, in consideration of the premises and the mutual
agreement herein set forth, the parties hereby agree as follows:

                  1. AMENDMENT OF SECTION 1(a). Section 1(a) of the Rights
Agreement is hereby amended to add the following sentence at the end thereof:

                  "Notwithstanding anything in this Agreement to the contrary,
                  (A) for so long as none of the KPENV Entities that have
                  reported or

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                  are required to report ownership on Schedule 13G or Schedule
                  13D under the Exchange Act (or any comparable or successor
                  report) takes, or states any intention or desire to take, any
                  action prohibited under any of clauses (a) through (f) of
                  Section 4.01 of the Investor Agreement or (B) (I) if any of
                  the KPENV Entities that have reported or are required to
                  report ownership on Schedule 13G or Schedule 13D under the
                  Exchange Act (or any comparable or successor report) takes, or
                  states any intention or desire to take, any action prohibited
                  under any of clauses (a) through (f) of Section 4.01 of the
                  Investor Agreement and (II) the Board of Directors of the
                  Company in its sole discretion adopts a resolution approving
                  such action (which resolution may be adopted prior to, upon or
                  not later than 15 days following such time as a majority of
                  the Board of Directors of the Company becomes aware of the
                  taking of any such action by any KPENV Entity), none of the
                  KPENV Entities shall be deemed to be an Acquiring Person
                  solely as a consequence of: (i) the execution of the FEI
                  Merger Agreement; (ii) the beneficial ownership by the KPENV
                  Entities of Common Stock or other securities of the Company
                  acquired directly as a result of the FEI Merger; (iii) the
                  beneficial ownership by the KPENV Entities of the Philips
                  Option Shares; (iv) the acquisition by, or beneficial
                  ownership of, the KPENV Entities of a number of shares of
                  Common Stock, in addition to the shares described in clauses
                  (ii) and (iii), that is equal to or less than one percent (1%)
                  of the total number of shares of Common Stock from time to
                  time outstanding, calculated on a primary basis; and/or (v)
                  the transfer of shares of Common Stock received pursuant to
                  (ii), (iii) or (iv) above by and among the KPENV Entities."

                  2. AMENDMENT OF SECTION 1(kk). Section 1(kk) of the Rights
Agreement is hereby amended to add the following proviso at the end thereof:

                  "; PROVIDED FURTHER, HOWEVER, that (A) for so long as none of
                  the KPENV Entities that have reported or are required to
                  report ownership on Schedule 13G or Schedule 13D under the
                  Exchange Act (or any comparable or successor report) takes, or
                  states any intention or desire to take, any action prohibited
                  under any of clauses (a) through (f) of Section 4.01 of the
                  Investor Agreement or (B)(I) if any of the KPENV Entities that
                  have reported or are required to report ownership on Schedule
                  13G or Schedule 13D under the Exchange Act (or any comparable
                  or successor report) takes, or states any intention or desire
                  to take, any action prohibited under any of clauses (a)
                  through (f) of Section 4.01 of the Investor Agreement and (II)
                  the Board of Directors of

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                  the Company in its sole discretion adopts a resolution
                  approving such action (which resolution may be adopted prior
                  to, upon or not later than 15 days following such time as a
                  majority of the Board of Directors of the Company becomes
                  aware of the taking of any such action by any KPENV Entity),
                  no Triggering Event shall result solely by virtue of: (i) the
                  execution of the FEI Merger Agreement; (ii) the beneficial
                  ownership by the KPENV Entities of Common Stock or other
                  securities of the Company acquired directly as a result of the
                  FEI Merger; (iii) the beneficial ownership by the KPENV
                  Entities of the Philips Option Shares; (iv) the acquisition
                  by, or beneficial ownership of, the KPENV Entities of a number
                  of shares of Common Stock, in addition to the shares described
                  in clauses (ii) and (iii), that is equal to or less than one
                  percent (1%) of the total number of shares of Common Stock
                  from time to time outstanding, calculated on a primary basis;
                  and/or (v) the transfer of shares of Common Stock received
                  pursuant to (ii), (iii) or (iv) above by and among the KPENV
                  Entities."

                  3. AMENDMENT OF SECTION 1. Section 1 of the Rights Agreement
is hereby amended to add the following subparagraphs at the end thereof:

                     (pp) "Acquisition" shall mean Venice Acquisition Corp., an
                  Oregon corporation and a wholly-owned subsidiary of the
                  Company.

                     (qq) "FEI" shall mean FEI Company, an Oregon corporation.

                     (rr) "FEI Merger" shall mean the merger of Acquisition with
                  and into FEI pursuant to the FEI Merger Agreement with the
                  result that FEI will be the surviving corporation and shall
                  become a wholly-owned subsidiary of the Company.

                     (ss) "FEI Merger Agreement" shall have the meaning set
                  forth in Section 36 hereof.

                     (tt) "Investor Agreement"shall mean that certain Investor
                  Agreement, dated as of the date hereof, by and between the
                  Company, Philips Business Electronics International B.V. and
                  FEI.

                     (uu) "KPENV Entities" shall mean, collectively, Koninklijke
                  Philips Electronics N.V., a company incorporated under the
                  laws of the Netherlands, and each entity controlled by
                  Koninklijke Philips Electronics N.V.

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                     (vv) "Philips Option Shares" shall mean securities issuable
                  to Philips pursuant to Section 2.03 of the Investor Agreement.

                  4. AMENDMENT OF SECTION 3(a). Section 3(a) of the Rights
Agreement is hereby amended to add the following sentence at the end thereof:

                  "Notwithstanding anything in this Agreement to the
                  contrary,(A) for so long as none of the KPENV Entities that
                  have reported or are required to report ownership on Schedule
                  13G or Schedule 13D under the Exchange Act (or any comparable
                  or successor report) takes, or states any intention or desire
                  to take, any action prohibited under any of clauses (a)
                  through (f) of Section 4.01 of the Investor Agreement or
                  (B)(I) if any of the KPENV Entities that have reported or are
                  required to report ownership on Schedule 13G or Schedule 13D
                  under the Exchange Act (or any comparable or successor report)
                  takes, or states any intention or desire to take, any action
                  prohibited under any of clauses (a) through (f) of Section
                  4.01 of the Investor Agreement and (II) the Board of Directors
                  of the Company in its sole discretion adopts a resolution
                  approving such action (which resolution may be adopted prior
                  to, upon or not later than 15 days following such time as a
                  majority of the Board of Directors of the Company becomes
                  aware of the taking of any such action by any KPENV Entity), a
                  Distribution Date shall not be deemed to have occurred solely
                  by virtue of: (i) the execution of the FEI Merger Agreement;
                  (ii) the beneficial ownership by the KPENV Entities of Common
                  Stock or other securities of the Company acquired directly as
                  a result of the FEI Merger; (iii) the beneficial ownership by
                  the KPENV Entities of the Philips Option Shares; (iv) the
                  acquisition by, or beneficial ownership of, the KPENV Entities
                  of a number of shares of Common Stock, in addition to the
                  shares described in clauses (ii) and (iii), that is equal to
                  or less than one percent (1%) of the total number of shares of
                  Common Stock from time to time outstanding, calculated on a
                  primary basis; and/or (v) the transfer of shares of Common
                  Stock received pursuant to (ii), (iii) or (iv) above by and
                  among the KPENV Entities."

                  5. AMENDMENT OF SECTION 7(a). Section 7(a) of the Rights
Agreement is hereby amended to add the following sentence at the end thereof:

                  "Notwithstanding anything in this Agreement to the
                  contrary,(A) for so long as none of the KPENV Entities that
                  have reported or are required to report ownership on Schedule
                  13G or Schedule 13D under the

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                  Exchange Act (or any comparable or successor report)
                  takes, or states any intention or desire to take, any action
                  prohibited under any of clauses (a) through (f) of Section
                  4.01 of the Investor Agreement or (B)(I) if any of the KPENV
                  Entities that have reported or are required to report
                  ownership on Schedule 13G or Schedule 13D under the Exchange
                  Act (or any comparable or successor report) takes, or states
                  any intention or desire to take, any action prohibited under
                  any of clauses (a) through (f) of Section 4.01 of the Investor
                  Agreement and (II) the Board of Directors of the Company in
                  its sole discretion adopts a resolution approving such action
                  (which resolution may be adopted prior to, upon or not later
                  than 15 days following such time as a majority of the Board of
                  Directors of the Company becomes aware of the taking of any
                  such action by any KPENV Entity), none of the following shall
                  be deemed to be events that cause the Rights to become
                  exercisable pursuant to the provisions of this Section 7 or
                  otherwise: (i) the execution of the FEI Merger Agreement; (ii)
                  the beneficial ownership by the KPENV Entities of Common Stock
                  or other securities of the Company acquired directly as a
                  result of the FEI Merger; (iii) the beneficial ownership by
                  the KPENV Entities of the Philips Option Shares; (iv) the
                  acquisition by, or beneficial ownership of, the KPENV Entities
                  of a number of shares of Common Stock, in addition to the
                  shares described in clauses (ii) and (iii), that is equal to
                  or less than one percent (1%) of the total number of shares of
                  Common Stock from time to time outstanding, calculated on a
                  primary basis; and/or (v) the transfer of shares of Common
                  Stock received pursuant to (ii), (iii) or (iv) above by and
                  among the KPENV Entities."

                  6. ADDITION OF SECTION 36. The Rights Agreement is hereby
amended to add the following new Section 36:

                  "Section 36.  MERGER WITH FEI

                     The Company, Acquisition and FEI have entered into an
                  Agreement and Plan of Merger, dated as of July 11, 2002, as it
                  may be amended from time to time (the "FEI Merger Agreement").
                  Notwithstanding anything in this Agreement to the contrary, if
                  the FEI Merger Agreement shall be terminated for any reason,
                  then, effective as of the time of such termination, the
                  following provisions which were added to this Agreement by
                  Amendment No. 2 to Rights Agreement, dated as of July 11,
                  2002, shall be deemed repealed and deleted without any further
                  action on the part of the Company or the Rights Agent: (1) the
                  last sentence of Section 1(a) hereof, (2) the proviso at the
                  end of Section 1(kk) hereof, (3) subsections (pp), (qq), (rr),
                  (ss), (tt), (uu) and (vv) of Section 1 hereof, (4) the last
                  sentence of Section 3(a) hereof and (5) the last sentence of
                  Section 7(a) hereof."

                  7. EFFECTIVENESS. This Amendment No. 2 shall be deemed
effective as of the date first written above. Except as amended hereby, the
Rights Agreement shall remain in full force

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and effect and shall be otherwise unaffected hereby.

                  8. MISCELLANEOUS. This Amendment No. 2 shall be deemed to be a
contract made under the laws of the State of Delaware and for all purposes shall
be governed by and construed in accordance with the laws of such state
applicable to contracts to be made and performed entirely within such state
without giving effect to the principles of conflict of laws thereof. This
Amendment No. 2 may be executed in any number of counterparts, each of such
counterparts shall for all purposes be deemed to be an original, and all such
counterparts shall together constitute but one and the same instrument. If any
term or other provision of this Amendment No. 2 is determined to be invalid,
illegal or incapable of being enforced by any rule of law, or public policy, all
other terms and provisions of this Amendment No. 2 shall nevertheless remain in
full force and effect and upon such determination that any term or other
provision is invalid, illegal or incapable of being enforced, this Amendment No.
2 and such term or other provision shall be deemed to have been amended so as to
effect the original intent of the parties as closely as possible in a manner
acceptable to the board of directors of the Company.

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                  IN WITNESS WHEREOF, this Amendment No. 2 to Rights Agreement
is executed under seal as of the date first set forth above.

                                 VEECO INSTRUMENTS INC.


                                 By: /s/ Greg Robbins
                                     -------------------------------------------
                                     Name:  Greg Robbins
                                     Title: Vice President and General Counsel


                                 AMERICAN STOCK TRANSFER AND TRUST
                                 COMPANY


                                 By: /s/ Herbert J. Lemmer
                                     -------------------------------------------
                                     Name:  Herbert J. Lemmer
                                     Title:  Vice President and General Counsel