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                                                                     Exhibit 4.1


                          AMENDMENT TO RIGHTS AGREEMENT

                  This AMENDMENT (the "Amendment") is being entered into as of
September 6, 2001, 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 (the "Rights Agreement");

                  WHEREAS, it is proposed that the Company enter into an
Agreement and Plan of Merger (the "AE Merger Agreement") by and among the
Company, Veeco Acquisition Corp., a Minnesota corporation and a wholly owned
subsidiary of the Company ("Veeco Acquisition"), Applied Epi, Inc., a Minnesota
corporation ("Applied Epi"), and certain Applied Epi security holders pursuant
to which Veeco Acquisition will merge with and into Applied Epi with the result
that Applied Epi will be the surviving corporation and shall become a wholly
owned subsidiary of the Company (the "AE Merger");

                  WHEREAS, pursuant to the AE Merger, Paul E. Colombo, Founder
and Chairman of Applied Epi, will receive 3,646,969 shares of common stock and
other securities of the Company, representing approximately 14.7% of the
outstanding shares of common stock of the Company as of September 6, 2001; 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 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,
                  for so long as Paul E. Colombo and/or any of his existing or
                  future Affiliates or Associates 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)
                  and do not state any intention to, or reserve the right to,
                  control or influence the management or policies of the Company
                  or engage in any of the actions specified in Item 4 of
                  Schedule 13D (other than the disposition of the Common Stock),
                  none of Paul E. Colombo or any of his existing or future
                  Affiliates or Associates shall be deemed to be an Acquiring
                  Person solely by virtue of: (i) the execution of the AE Merger
                  Agreement; (ii) the acquisition of Common Stock or other
                  securities of the Company by Paul E. Colombo or his existing
                  or future Affiliates or Associates


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                  pursuant to the AE Merger; (iii) the grant by the Company of
                  options to purchase Common Stock to Paul E. Colombo or his
                  existing or future Affiliates or Associates in their capacity
                  as consultants, employees or directors of the Company, or the
                  exercise of such options; (iv) the acquisition by Paul E.
                  Colombo or his existing or future Affiliates or Associates of
                  up to one percent (1%) of the shares of Common Stock then
                  outstanding in excess of the percentage of shares of Common
                  Stock beneficially owned by Paul E. Colombo or his existing or
                  future Affiliates or Associates under clauses (i), (ii) and
                  (iii) above; and/or (v) the transfer of shares of Common Stock
                  received pursuant to (ii), (iii) or (iv) above by and among
                  Paul E. Colombo and/or any of his existing or future
                  Affiliates or Associates."

                  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, HOWEVER, that for so long as Paul E. Colombo
                  and/or any of his existing or future Affiliates or Associates
                  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) and do not state any intention
                  to, or reserve the right to, control or influence the
                  management or policies of the Company or engage in any of the
                  actions specified in Item 4 of Schedule 13D (other than the
                  disposition of the Common Stock), no Triggering Event shall
                  result solely by virtue of: (i) the execution of the AE Merger
                  Agreement; (ii) the acquisition of Common Stock or other
                  securities of the Company by Paul E. Colombo or his existing
                  or future Affiliates or Associates pursuant to the AE Merger;
                  (iii) the grant by the Company of options to purchase Common
                  Stock to Paul E. Colombo or his existing or future Affiliates
                  or Associates in their capacity as consultants, employees or
                  directors of the Company, or the exercise of such options;
                  (iv) the acquisition by Paul E. Colombo or his existing or
                  future Affiliates or Associates of up to one percent (1%) of
                  the shares of Common Stock then outstanding in excess of the
                  percentage of shares of Common Stock beneficially owned by
                  Paul E. Colombo or his existing or future Affiliates or
                  Associates under clauses (i), (ii) and (iii) above; and/or (v)
                  the transfer of shares of Common Stock received pursuant to
                  (ii), (iii) or (iv) above by and among Paul E. Colombo and/or
                  any of his existing or future Affiliates or Associates."

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

                           (ll) "Applied Epi" shall mean Applied Epi, Inc., a
                  Minnesota corporation.

                           (mm) "AE Merger" shall mean the merger of Veeco
                  Acquisition with and into Applied Epi pursuant to the AE
                  Merger Agreement with the result that Applied Epi will be the
                  surviving corporation and shall become a wholly owned
                  subsidiary of the Company.



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                           (nn) "AE Merger Agreement" shall have the meaning set
                  forth in Section 35 hereof.

                           (oo) "Veeco Acquisition" shall mean Veeco Acquisition
                  Corp., a Minnesota corporation and a wholly owned subsidiary
                  of the Company.

                  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,
                  for so long as Paul E. Colombo and/or any of his existing or
                  future Affiliates or Associates 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)
                  and do not state any intention to, or reserve the right to,
                  control or influence the management or policies of the Company
                  or engage in any of the actions specified in Item 4 of
                  Schedule 13D (other than the disposition of the Common Stock),
                  a Distribution Date shall not be deemed to have occurred
                  solely by virtue of: (i) the execution of the AE Merger
                  Agreement; (ii) the acquisition of Common Stock or other
                  securities of the Company by Paul E. Colombo or his existing
                  or future Affiliates or Associates pursuant to the AE Merger;
                  (iii) the grant by the Company of options to purchase Common
                  Stock to Paul E. Colombo or his existing or future Affiliates
                  or Associates in their capacity as consultants, employees or
                  directors of the Company, or the exercise of such options;
                  (iv) the acquisition by Paul E. Colombo or his existing or
                  future Affiliates or Associates of up to one percent (1%) of
                  the shares of Common Stock then outstanding in excess of the
                  percentage of shares of Common Stock beneficially owned by
                  Paul E. Colombo or his existing or future Affiliates or
                  Associates under clauses (i), (ii) and (iii) above; and/or (v)
                  the transfer of shares of Common Stock received pursuant to
                  (ii), (iii) or (iv) above by and among Paul E. Colombo and/or
                  any of his existing or future Affiliates or Associates."

                  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,
                  for so long as Paul E. Colombo and/or any of his existing or
                  future Affiliates or Associates 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)
                  and do not state any intention to, or reserve the right to,
                  control or influence the management or policies of the Company
                  or engage in any of the actions specified in Item 4 of
                  Schedule 13D (other than the disposition of the Common Stock),
                  none of: (i) the execution of the AE Merger Agreement; (ii)
                  the acquisition of Common Stock or other securities of the
                  Company by Paul E. Colombo or his existing or future
                  Affiliates or Associates pursuant to the AE Merger; (iii) the
                  grant by the Company of options to purchase Common Stock to
                  Paul E. Colombo or his existing or future Affiliates or
                  Associates in their capacity as consultants, employees or
                  directors of the Company, or the exercise of such options;
                  (iv) the acquisition by Paul E. Colombo or his existing or
                  future Affiliates or Associates


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                  of up to one percent (1%) of the shares of Common Stock then
                  outstanding in excess of the percentage of shares of Common
                  Stock beneficially owned by Paul E. Colombo or his existing or
                  future Affiliates or Associates under clauses (i), (ii) and
                  (iii) above; and/or (v) the transfer of shares of Common Stock
                  received pursuant to (ii), (iii) or (iv) above by and among
                  Paul E. Colombo and/or any of his existing or future
                  Affiliates or Associates shall be deemed to be events that
                  cause the Rights to become exercisable pursuant to the
                  provisions of this Section 7 or otherwise."

                  6. AMENDMENT OF SECTION 11. Section 11 of the Rights Agreement
is hereby amended to add the following sentence after the first sentence of said
Section:

                  "Notwithstanding anything in this Agreement to the contrary,
                  for so long as Paul E. Colombo and/or any of his existing or
                  future Affiliates or Associates 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)
                  and do not state any intention to, or reserve the right to,
                  control or influence the management or policies of the Company
                  or engage in any of the actions specified in Item 4 of
                  Schedule 13D (other than the disposition of the Common Stock),
                  none of: (i) the execution of the AE Merger Agreement; (ii)
                  the acquisition of Common Stock or other securities of the
                  Company by Paul E. Colombo or his existing or future
                  Affiliates or Associates pursuant to the AE Merger; (iii) the
                  grant by the Company of options to purchase Common Stock to
                  Paul E. Colombo or his existing or future Affiliates or
                  Associates in their capacity as consultants, employees or
                  directors of the Company, or the exercise of such options;
                  (iv) the acquisition by Paul E. Colombo or his existing or
                  future Affiliates or Associates of up to one percent (1%) of
                  the shares of Common Stock then outstanding in excess of the
                  percentage of shares of Common Stock beneficially owned by
                  Paul E. Colombo or his existing or future Affiliates or
                  Associates under clauses (i), (ii) and (iii) above; and/or (v)
                  the transfer of shares of Common Stock received pursuant to
                  (ii), (iii) or (iv) above by and among Paul E. Colombo and/or
                  any of his existing or future Affiliates or Associates shall
                  be deemed to be events of the type described in this Section
                  11 or to cause the Rights to be adjusted or to become
                  exercisable in accordance with this Section 11."

                  7. ADDITION OF SECTION 35. The Rights Agreement is hereby
amended to add the following new Section 35:

                  "Section 35.  MERGER WITH APPLIED EPI

                           The Company, Veeco Acquisition and Applied Epi have
                  entered into an Agreement and Plan of Merger, dated as of
                  September 6, 2001, as it may be amended from time to time (the
                  "AE Merger Agreement"). Notwithstanding anything in this
                  Agreement to the contrary, if the AE 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 the Amendment to Rights Agreement, dated as
                  of September 6, 2001, shall be deemed repealed and deleted
                  without any further action on the part of the Company or the
                  Rights


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                  Agent: (1) the last sentence of Section 1(a) hereof, (2) the
                  proviso at the end of Section 1(kk) hereof, (3) subsections
                  (ll), (mm), (nn) and (oo) of Section 1 hereof, (4) the last
                  sentence of Section 3(a) hereof, (5) the last sentence of
                  Section 7(a) hereof and (6) the second sentence of Section 11
                  hereof."

                  8. EFFECTIVENESS. This Amendment shall be deemed effective as
of the date first written above. Except as amended hereby, the Rights Agreement
shall remain in full force and effect and shall be otherwise unaffected hereby.

                  9. MISCELLANEOUS. This Amendment 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 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 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 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 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 an acceptable manner to
the board of directors of the Company.



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                  IN WITNESS WHEREOF, this Amendment to the Rights Agreement is
executed under seal as of the date first set forth above.

                                            VEECO INSTRUMENTS INC.


                                            By: /s/ Edward H. Braun
                                                --------------------------------
                                            Name:  Edward H. Braun
                                            Title: Chief Executive Officer and
                                                   President



                                            AMERICAN STOCK TRANSFER AND
                                            TRUST COMPANY


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



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