<PAGE>   1

                                                                     EXHIBIT 3.1

                      RESTATED CERTIFICATE OF INCORPORATION

                                       OF

                       GALILEO ELECTRO-OPTICS CORPORATION

     Galileo Electro-Optics Corporation, a corporation originally incorporated
under the General Corporation Laws of the State of Delaware on September 24,
1973 (the "Corporation"), does hereby certify:

     FIRST: That the Board of Directors of the Corporation by unanimous written
consent adopted the following vote proposing and declaring advisable the
following Amendment and Restatement of the Certificate of Incorporation of the
Corporation and directing that said amendment be submitted to the stockholders
of the Corporation for approval without a meeting in accordance with Section
228(a) of the General Corporation Laws of the State of Delaware:

     Voted: That the Certificate of Incorporation of the Corporation be amended
and restated in its entirety so as to supersede the original Certificate of
Incorporation and all amendments thereto so that, as amended and restated, the
Certificate shall read as follows:

                      RESTATED CERTIFICATE OF INCORPORATION

                                       OF

                       GALILEO ELECTRO-OPTICS CORPORATION

          FIRST: The name of the Corporation is Galileo Electro-Optics
     Corporation.

          SECOND: The registered office of the Corporation in the State of
     Delaware is located at No. 100 West 10th Street in the City of Wilmington,
     County of New Castle. The name and address of its registered agent is The
     Corporation Trust

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     Company, No. 100 West 10th Street, Wilmington, Delaware.

          THIRD: The purpose of the Corporation is to engage in any lawful act
     or activity for which corporations may be organized under the General
     Corporation Law of the State of Delaware.

          FOURTH: The total number of shares of stock which the Corporation
     shall have authority to issue is three million (3,000,000) shares of Common
     Stock of the par value of One Cent ($.01) each, amounting in the aggregate
     to Thirty Thousand Dollars ($30,0000).

          FIFTH: The affirmative vote or consent of two-thirds (66 2/3%) of the
     outstanding Common Stock of the Corporation shall be necessary to approve
     (a) any merger, consolidation, dissolution or liquidation of the
     Corporation, (b) the sale of substantially all of its assets, or (c) any
     amendment to this Certificate of Incorporation.

          SIXTH: The name and place of residence of the Incorporator is as
     follows:
  
                  Name                           Place of Residence  
                  ----                           ------------------
          Richard M. C. Glenn, III               29 Rumstick Road
                                                 Barrington, RI 02806
                                    
          SEVENTH: The Corporation is to have perpetual existence.

          EIGHTH: In furtherance and not in limitation of the powers conferred
     by the laws of the State of Delaware, the Board of Directors of the
     Corporation is authorized and empowered to make, alter, amend and repeal
     the Bylaws of the Corporation in any manner not inconsistent with the laws
     of the State of Delaware. The election of directors may but need not be by
     ballot unless the Bylaws so require.

          NINTH: The Corporation shall indemnify its officers, directors,
     employees and agents to the extent permitted by the General Corporation Law
     of Delaware.

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     SECOND: That the written consent to said Amendment and Restatement was
given by the stockholders of the Corporation in accordance with Section 228(a)
of the General Corporation Laws of the State of Delaware.

     THIRD: That the said Amendment and Restatement of Certificate of
Incorporation of Galileo Electro-Optics Corporation was duly adopted in
accordance with Sections 242 and 245 of the General Corporation Laws of the
State of Delaware by the written consent of the holders of greater than 66 2/3
percent of the issued and outstanding Common Stock of the Corporation. 

     IN WITNESS WHEREOF, Galileo Electro-Optics Corporation has caused this
Certificate to be signed by John D. White, President of the Corporation, and
attested by Richard M. C. Glenn III, its Secretary as of the 24th day of
November, 1982.


ATTEST:                                     GALILEO ELECTRO-OPTICS CORPORATION

/s/ Richard M.C. Glenn III                  By: /s/ John D. White
    --------------------------                  ----------------------
    Secretary                                       President



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                            CERTIFICATE OF AMENDMENT

                                       TO

                      RESTATED CERTIFICATE OF INCORPORATION

                                       OF

                       GALILEO ELECTRO-OPTICS CORPORATION

     Galileo Electro-Optics Corporation, a corporation organized and existing
under the General Corporation Laws of the State of Delaware, (the "Corporation")
does hereby certify:

     FIRST: That the Board of Directors of the Corporation, at a meeting duly
held, adopted the following vote proposing and declaring advisable the following
amendment to the Restated Certificate of Incorporation of the Corporation and
directed that said amendment be submitted to the stockholders of the Corporation
for approval without a meeting in accordance with Section 228(a) of the General
Corporation Laws of the State of Delaware.

     Voted: That Article FIFTH of the Restated Certificate of Incorporation of
the Corporation be amended in its entirety to provide as follows:

                    FIFTH: The affirmative vote or consent of two-thirds (66
               2/3%) of the outstanding Common Stock of the Corporation shall be
               necessary to approve (a) any merger, consolidation, dissolution
               or liquidation of the Corporation, (b) the sale of substantially
               all of its assets, or (c) any amendment to this Certificate of
               Incorporation which would modify this Article FIFTH.

     SECOND: That the written consent to said amendment and restatement was
given by the stockholders of the Corporation in accordance with Section 228(a)
of the General Corporation Laws of the State of Delaware.


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     THIRD: That the said Amendment to the Restated Certificate of Incorporation
of Galileo Electro-Optics Corporation was duly adopted in accordance with
Section 242 of the General Corporation Laws of the State of Delaware by the
written consent of the holders of greater than 66 2/3% of the issued and
outstanding Common Stock of the Corporation.

     IN WITNESS WHEREOF, Galileo Electro-Optics Corporation has caused this
Certificate to be signed by John B. White, President of the Corporation, and
attested by Richard M.C. Glenn, III, its Secretary as of the 3rd day of
February, 1983.

ATTEST:                             GALILEO ELECTRO-OPTICS CORPORATION


/s/ Richard M.C. Glenn, III         By: /s/ John D. White
---------------------------         ----------------------------------
    Secretary                               President



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                                   CERTIFICATE

             FOR RENEWAL AND REVIVAL OF CERTIFICATE OF INCORPORATION


     Galileo Electro-Optics Corporation, a corporation organized under the laws
of Delaware, The Certificate of Incorporation of which was filed in the office
of the Secretary of State on the 24th day of September, 1973, the Certificate of
Incorporation of which was voided for non-payment of taxes, now desires to
procure a restoration, renewal and revival of its Certificate of Incorporation,
and hereby certifies as follows:

1. The name of this corporation is Galileo Electro-Optics Corporation.

2. Its registered office in the State of Delaware is located at Corporation
Trust Center, 1209 Orange Street, City of Wilmington, County of New Castle and
the name of its registered agent at such address is The Corporation Trust
Company.

3. The date when the restoration, renewal, and revival of the Certificate of
Incorporation of this company is to commence is the 29th day of February A.D.
1984, same being prior to the date of the expiration of the Certificate of
Incorporation. This renewal and revival of the Certificate of Incorporation of
this corporation is to be perpetual.

4. This corporation was duly organized under the Laws of the State of Delaware
and carried on the business authorized by its Certificate of Incorporation until
the 1st day of March A.D. 1984, at which time its Certificate of Incorporation
becomes inoperative and void for non-payment of taxes and this certificate for
renewal and revival is filed by authority of the duly elected directors of the
corporation in accordance with the laws of the State of Delaware.

     IN WITNESS WHEREOF, said Galileo Electro-Optics Corporation in compliance
with Section 312 of Title 8 of the Delaware Code has caused this certificate to
be signed by Christopher H. Tosswill its last and acting Vice President and
attested by Richard M.C. 

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Glenn, III, its last and acting Secretary, this 29th day of January, 1985.

                                       GALILEO ELECTRO-OPTICS CORPORATION



                                       By: /s/ Christopher H. Tosswill
                                           ----------------------------------
                                               Last and Acting Vice President





ATTEST:


By: /s/ Richard M.C. Glenn III
    ------------------------------
        Last and Acting Secretary


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                            CERTIFICATE OF AMENDMENT
                                       TO
                      RESTATED CERTIFICATE OF INCORPORATION
                                       OF
                       GALILEO ELECTRO-OPTICS CORPORATION


     Galileo Electro-Optics Corporation, a corporation organized and existing
under the General Corporation Laws of the State of Delaware, (the "Corporation")
does hereby certify:

     First: That the Board of Directors of the Corporation, at a meeting duly
held, adopted the following votes proposing and declaring advisable the
following amendments to the Restated Certificate of Incorporation of the
Corporation and directed that said amendments be submitted to the stockholders
of the Corporation for approval at the Annual Meeting called in accordance with
Section 222 of the General Corporation Laws of the State of Delaware.

         VOTED:   That Article FOURTH of the Corporation's Restated Certificate
         -----    of Incorporation be amended to increase the number of
                  authorized shares of common stock from 3,000,000 to 18,000,000
                  so that Article FOURTH would read in its entirety as follows:

                  "FOURTH: The total number of shares of stock which the
                           Corporation shall have authority to issue is eighteen
                           million (18,000,000) shares of common stock of the
                           par value of One Cent ($.01) each, amounting in the
                           aggregate to One Hundred Eighty Thousand Dollars
                           ($180,000.00)."

         VOTED:   That Article NINTH of the Corporation's Certificate of
         -----    Incorporation be amended by adding a second sentence thereto
                  so that Article NINTH would read in its entirety as follows:

                  "NINTH:  The Corporation shall indemnify its officers,
                           directors, employees and agents to the extent
                           permitted by law. No director of the Corporation
                           shall be liable to the Corporation or its
                           stockholders for monetary damages for breach of
                           fiduciary duty as a director, except for


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                           liability (i) for any breach of the director's duty
                           of loyalty to the Corporation or its stockholders,
                           (ii) for acts or omissions not in good faith or which
                           involve intentional misconduct or a knowing violation
                           of law, (iii) under Section 174 of the Delaware
                           General Corporation Law, or (iv) for any transaction
                           from which the director derived an improper personal
                           benefit."

     Second: That said Amendments to the Restated Certificate of Incorporation
of Galileo Electro-Optics Corporation were duly adopted in accordance with
Section 242 of the General Corporation Laws of the State of Delaware by the
favorable vote of the majority of the holders of the issued and outstanding
common stock of the Corporation voting at the Annual Meeting.

     IN WITNESS WHEREOF, Galileo Electro-Optics Corporation has caused this
Certificate to be signed by William T. Hanley, President of the Corporation, and
attested by Richard M. C. Glenn, III, its Secretary as of the 10th day of
December, 1986.


ATTEST:                                   Galileo Electro-Optics Corporation


 /s/ Richard M.C. Glenn, III              By /s/ William T. Hanley
 ---------------------------                 -------------------------------
     Secretary                                   President


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                       CERTIFICATE OF OWNERSHIP AND MERGER

                                       of

                               GALILEO CORPORATION
                            (a Delaware corporation)

                                      into

                       GALILEO ELECTRO-OPTICS CORPORATION
                            (a Delaware corporation)

                              UNDER SECTION 253 OF
                      THE DELAWARE GENERAL CORPORATION LAW

Galileo Electro-Optics Corporation (the "Corporation"), a Delaware corporation,
hereby certifies that:

     1.   The Corporation is incorporated under the Delaware General Corporation
          Law.

     2.   The Corporation owns all of the outstanding shares of capital stock of
          Galileo Corporation, a Delaware corporation.

     3.   The Corporation by the following resolutions of its board of directors
          duly adopted on September 17, 1996 determined to merge Galileo
          Corporation into itself on the terms set forth in such resolutions:

          RESOLVED: To merge Galileo Corporation, a Delaware corporation all of
                    the outstanding stock of which is owned by this Corporation,
                    with and into this Corporation pursuant to Section 253 of
                    the Delaware General Corporation Law.

          RESOLVED: To change the name of this Corporation to Galileo
                    Corporation.

     IN WITNESS WHEREOF, the Corporation has caused this certificate to be
signed by its authorized officer on September 17, 1996.

                                          GALILEO ELECTRO-OPTICS CORPORATION

                                          By: /s/ William T. Hanley
                                                  William T. Hanley, President
                                                    and Chief Executive Officer



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                            CERTIFICATE OF AMENDMENT

                                       OF

                          CERTIFICATE OF INCORPORATION

                                       OF

                               GALILEO CORPORATION


     Galileo Corporation (the "Corporation"), a corporation organized and
existing under the Delaware General Corporation Law, does hereby certify as
follows:

     FIRST: A resolution was duly adopted at a meeting of the Board of Directors
of the Corporation setting forth a proposed amendment of the Certificate of
Incorporation of the Corporation, declaring such amendment to be advisable and
directing that it be considered at the next annual meeting of the stockholders
of the Corporation. The resolution setting forth the proposed amendment is as
follows:

          RESOLVED: that the Corporation's Certificate of Incorporation be
     amended by changing Article FOURTH to read as follows:

               The total number of shares of stock which the Corporation shall
          have authority to issue is thirty-six million (36,000,000) shares of
          common stock, one cent ($.01) par value.

     SECOND: Thereafter, pursuant to resolution of its Board of Directors, the
annual meeting of the stockholders of the Corporation was duly called and held
upon notice in accordance with Section 222 of the Delaware General Corporation
Law, at which meeting the necessary number of shares as required by statute were
voted in favor of the amendment.

     THIRD: Such amendment was duly adopted in accordance with the provisions of
Section 242 of the Delaware General Corporation Law.

     IN WITNESS WHEREOF, Galileo Corporation has caused this certificate to be
signed by William T. Hanley, its President, on January 14, 1997.

                                         /s/ William T. Hanley
                                         -------------------------------
                                             William T. Hanley
                                               President


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