<PAGE>
 
                                                                     EXHIBIT 3.2


                                      FORM

                                       of

               CERTIFICATE OF DESIGNATION, PREFERENCES AND RIGHTS

                                       of

                        SERIES A JUNIOR PREFERRED STOCK

                                       of

                          OPTICAL SENSORS INCORPORATED

                         Pursuant to Section 151 of the
           Delaware General Corporation Law of the State of Delaware

                               __________________

     We, Sam B. Humphries, Chief Executive Officer, and Wesley G. Peterson,
Chief Financial Officer, of Optical Sensors Incorporated, a corporation
organized and existing under the General Corporation Law of the State of
Delaware (the "Corporation"), in accordance with the provisions thereof, DO
HEREBY CERTIFY:

     That pursuant to the authority vested in the Board of Directors by the
Certificate of Incorporation of the Corporation, the said Board of Directors on
December 3, 1996, adopted the following resolution creating a series of two
hundred fifty thousand (250,000) shares of Preferred Stock designated as Series
A Junior Preferred Stock:

     RESOLVED, that pursuant to the authority vested in the Board of Directors
of this Corporation in accordance with the provisions of its Certificate of
Incorporation, a series of Preferred Stock of the Corporation be and it hereby
is created, and that the designation and amount thereof and the voting powers,
preferences and relative, participation, optional and other special rights of
the shares of such series, and the qualifications, limitation or restrictions
thereof are as follows:

     Section 1.  Designation and Amount.  The shares of such series shall be
                 ----------------------                                     
designated as Series A Junior Preferred Stock, par value $.01 per share (the
"Series A Junior Preferred Share(s)"), and the number of shares constituting
such series shall be two hundred fifty thousand (250,000).
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     Section 2.  Dividends and Distributions.
                 --------------------------- 

     (a)     Subject to the prior and superior rights of the holders of any
shares of any series of Preferred Stock ranking prior and superior to Series A
Junior Preferred Shares with respect to dividends, the holders of Series A
Junior Preferred Shares shall be entitled to receive, when, as and if declared
by the Board of Directors out of funds legally available for the purpose,
quarterly dividends payable in cash on the first day of January, March, July and
October in each year (each such date being referred to herein as a "Quarterly
Dividend Payment Date," commencing on the first Quarterly Dividend Payment Date
after the first issuance of a share or fraction of a Series A Junior Preferred
Share, in an amount per share (rounded to the nearest cent) equal to (subject to
the provision for adjustment hereinafter set forth), 1,000 times the aggregate
per share amount of all cash dividends, and 1,000 times the aggregate per share
amount (payable in kind) of all non-cash dividends or other distributions other
than a dividend payable in shares of Common Stock or a subdivision of the
outstanding shares of Common Stock (by reclassification or otherwise), declared
on the Common Stock, par value $.01 per share, of the Corporation (the "Common
Stock") since the immediately preceding Quarterly Dividend Payment Date, or,
with respect to the first Quarterly Dividend Payment Date, since the first
issuance of any share or fraction of a Series A Junior Preferred Share. In the
event the Corporation shall at any time after December 3, 1996 (the "Rights
Declaration Date") (i) declare any dividend on Common Stock payable in shares of
Common Stock, (ii) subdivide the outstanding Common Stock, or (iii) combine the
outstanding Common Stock into a smaller number of shares, then in each such case
the amount to which holders of Series A Junior Preferred Shares were entitled
immediately prior to such event under the preceding sentence shall be adjusted
by multiplying such amount by a fraction, the numerator of which is the number
of shares of Common Stock outstanding immediately after such event and the
denominator of which is the number of shares of Common Stock that were
outstanding immediately prior to such event.

     (b)     The Corporation shall declare a dividend or distribution on the
Series A Junior Preferred Shares as provided in paragraph (a) above immediately
after it declares a dividend or distribution on the Common Stock (other than a
dividend payable in shares of Common Stock).

     (c)     Dividends shall begin to accrue and be cumulative on outstanding
Series A Junior Preferred Shares from the Quarterly Dividend Payment Date next
preceding the date of issue of such Series A Junior Preferred Shares, unless the
date of issue of such shares is prior to the record date for the first Quarterly
Dividend Payment Date, in which case dividends on such shares shall begin to
accrue from the date of issue of such shares, or unless the date of issue is a
Quarterly Dividend Payment Date or is a date after the record date for the
determination of holders of Series A Junior Preferred Shares entitled to receive
a quarterly dividend and before such Quarterly Dividend Payment Date, in either
of which events such dividends shall begin to accrue and be cumulative from such
Quarterly Dividend Payment Date. Accrued but unpaid dividends shall not bear
interest. Dividends paid on the Series A Junior Preferred Shares in an amount
less than the total amount of such dividends at the time accrued and payable on
such shares shall be allocated pro rata on a share-by-share basis among all such
shares at the time outstanding. The Board of Directors may fix a record date for
the determination of holders of Series A Junior Preferred Shares entitled to
receive payment of a dividend or distribution declared thereon, which record
date shall be no more than 30 days prior to the date fixed for the payment
thereof.

     Section 3.  Voting Rights.  In addition to any other voting rights required
                 -------------                                                  
by law, the holders of Series A Junior Preferred Shares shall have the following
voting rights:

     (a)     Subject to the provision for adjustment hereinafter set forth, each
Series A Junior Preferred Share shall entitle the holder thereof to 1,000 votes
on all matters submitted to a vote of the stockholders of 


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the Corporation. In the event the Corporation shall at any time after the Rights
Declaration Date (i) declare any dividend on Common Stock payable in shares of
Common Stock, (ii) subdivide the outstanding shares of Common Stock, or (iii)
combine the outstanding shares of Common Stock into a smaller number of shares,
then in each such case the number of votes per share to which holders of Series
A Junior Preferred Shares were entitled immediately prior to such event shall be
adjusted by multiplying such number by a fraction, the numerator of which is the
number of shares of Common Stock outstanding immediately after such event and
the denominator of which is the number of shares of Common Stock that were
outstanding immediately prior to such event.

     (b)     If, on the date used to determine stockholders of record for any
meeting of stockholders for the election of directors, a default in dividends on
the Series A Junior Preferred Shares shall exist, the number of directors
constituting the Board of Directors of the Corporation shall be increased by
two, and the holders of the Series A  Junior Preferred Shares shall have the
right at such meeting, voting together as a single class, to elect two directors
of the Corporation to fill such newly created directorships.  Each director
elected by the holders of Series A Junior Preferred Shares (herein called a
"Series A Preferred Director") shall continue to serve as such director for the
full term for which he shall have been elected, notwithstanding that prior to
the end of such term a default in dividends shall cease to exist.  Any Series A
Preferred Director may be removed by, and shall not be removed except by, the
vote of the holders of record of the outstanding Series A Junior Preferred
Shares, voting together as a single class, at a meeting of the stockholders, or
of the holders of Series A Junior Preferred Shares called for such purpose.
Thereafter, so long as a default in dividends on the Series A Preferred Shares
shall exist (i) any vacancy in the office of a Series A Preferred Director may
be filled (except as provided in the following clause (ii)) by an instrument in
writing signed by the remaining Series A Preferred Director and filed with the
Corporation and (ii) in the case of the removal of any Series A Preferred
Director, the vacancy may be filled by the vote of the holders of the
outstanding Series A Junior Preferred Shares, voting together as a class, at the
same meeting at which such removal shall be voted.  Each director appointed as
aforesaid by the remaining Series A Preferred Director shall be deemed, for all
purposes hereof, to be a Series A Preferred Director.  Whenever the term of
office of the Series A Preferred Directors shall end and no default in dividends
on the Series A Junior Preferred Shares shall exist, the number of directors
constituting the Board of Directors of the Corporation shall be reduced by two.
For the purposes of this Section 3(b), a "default in dividends" on the Series A
Junior Preferred Shares shall be deemed to have occurred whenever there shall be
an arrearage in the payment of any dividends to which the holders of the Series
A Junior Preferred Shares are entitled to receive, whether or not any such
dividends have been declared by the Board of Directors, for six consecutive
quarters, and, having so occurred, such default shall be deemed to exist
thereafter until, but only until, all accrued dividends on all shares of Series
A Junior Preferred Shares then outstanding shall have been paid through the last
Quarterly Dividend Payment Date.

             At any time when such right to elect directors separately as a
class shall have so vested, the Corporation may, and upon the written request of
the holders of record of not less than 20% of the then outstanding total number
of the Series A Junior Preferred Shares shall, call a special meeting of holders
of such Series A Junior Preferred Shares for the election of directors. In the
case of such a written request, such special meeting shall be held within 90
days after the delivery of such request, and, in either case, at the place and
upon the notice provided by law and in the Bylaws of the Corporation; provided
that the Corporation shall not be required to call such a special meeting if
such request is received less than 120 days before the date fixed for the next
ensuing annual or special meeting of stockholders of the Corporation. After the
number of directors of the Corporation shall have been increased by two as
hereinabove provided, the number as so increased may thereafter be further
increased or decreased in such manner as may be permitted by the Certificate of
Incorporation or By-laws, provided that no such action 

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shall impair the right of the holders of Series A Junior Preferred Shares to
elect and to be represented by two directors as herein provided.

     (c)     Except as otherwise provided herein, in the Certificate of
Incorporation of the Corporation or by law, the holders of Series A Junior
Preferred Shares and the holders of Common Stock (and the holders of shares of
any other series or class entitled to vote thereon) shall vote together as one
class on all matters submitted to a vote of stockholders of the Corporation.

     Section 4.  Certain Restrictions.
                 -------------------- 

     (a)     Whenever any dividends or other distributions payable on the Series
A Junior Preferred shares as provided in Section 2 are in arrears, thereafter
and until all accrued and unpaid dividends and distributions, whether or not
declared, on Series A Junior Preferred Shares outstanding shall have been paid
in full, the Corporation shall not:

          (i)    declare or pay dividends on, make any other distributions on,
     or redeem or purchase or otherwise acquire for consideration any share
     ranking junior (either as to dividends or upon liquidation, dissolution or
     winding up) to the Series A Junior Preferred Shares;

          (ii)   declare or pay dividends on or make any other distributions on
     any shares of stock ranking on a parity (either as to dividends or  upon
     liquidation, dissolution or winding up) with the Series A Junior Preferred
     Shares, except dividends paid ratably on the Series A Junior Preferred
     Shares and all such parity stock on which dividends are payable or in
     arrears in proportion to the total amounts to which the holders of all such
     shares are then entitled;

          (iii)  redeem or purchase or otherwise acquire for consideration
     shares of any stock ranking on a parity (either as to dividends or upon
     liquidation, dissolution or winding up) with the Series A Junior Preferred
     Shares, provided that the Corporation may at any time redeem, purchase or
     otherwise acquire shares of any such parity stock in exchange for shares of
     any stock of the Corporation ranking junior (either as to dividends or upon
     dissolution, liquidation or winding up) to the Series A Junior Preferred
     Shares; or

          (iv)   purchase or otherwise acquire for consideration any Series A
     Junior Preferred Shares, except in accordance with a purchase offer made in
     writing or by publication (as determined by the Board of Directors) to all
     holders of such shares upon such terms as the Board of Directors, after
     consideration of the respective annual dividend rates and other relative
     rights and preferences of the respective series and classes, shall
     determine in good faith will result in fair and equitable treatment among
     the respective series or classes.

     (b)     The Corporation shall not permit any subsidiary of the Corporation
to purchase or otherwise acquire for consideration any shares of stock of the
Corporation unless the Corporation could, under paragraph (a) of this Section 4,
purchase or otherwise acquire such shares at such time and in such manner.

     Section 5.  Reacquired Shares.  Any Series A Junior Preferred Shares
                 -----------------                                       
purchased or otherwise acquired by the Corporation in any manner whatsoever
shall be retired and cancelled promptly after the acquisition thereof.  All such
shares shall upon their cancellation become authorized but unissued Preferred
Stock and may be reissued as part of a new series of Preferred Stock to be
created by resolution or resolutions of the Board of Directors.


                                       4
<PAGE>
 
     Section 6.  Liquidation, Dissolution or Winding Up.  In the event of any
                 --------------------------------------                      
voluntary or involuntary liquidation, dissolution or winding up of the
Corporation, the holders of Series A Junior Preferred Shares shall be entitled
to receive the greater of (a) $1,000.00 per share, plus accrued dividends to the
date of distribution, whether or not earned or declared, or (b) an amount per
share, subject to the provision for adjustment hereinafter set forth, equal to
1,000 times the aggregate amount to be distributed per share to holders of
Common Stock.  In the event the Corporation shall at any time after the Rights
Declaration Date (i) declare any dividend on Common Stock payable in shares of
Common Stock, (ii) subdivide the outstanding shares of Common Stock, or (iii)
combine the outstanding shares of Common Stock into a smaller number of shares,
then in each such case the amount to which holders of Series A Junior Preferred
Shares were entitled immediately prior to such event pursuant to clause (b) of
the preceding sentence shall be adjusted by multiplying such amount by a
fraction, the numerator of which is the number of shares of Common Stock
outstanding immediately after such event and the denominator of which is the
number of shares of Common Stock that were outstanding immediately prior to such
event.

     Section 7.  Consolidation, Merger, Etc.  In case the Corporation shall
                 --------------------------                                
enter into any consolidation, merger, combination or other transaction in which
the shares of Common Stock are exchanged for or changed into other stock or
securities, cash and/or any other property, then in any such case the Series A
Junior Preferred Shares shall at the same time be similarly exchanged or changed
in an amount per share (subject to the provision for adjustment hereinafter set
forth) equal to 1,000 times the aggregate amount of stock, securities, cash
and/or any other property (payable in kind), as the case may be, into which or
for which each share of Common Stock is changed or exchanged.  In the event the
Corporation shall at any time after the Rights Declaration Date (i) declare any
dividend on Common Stock payable in shares of Common Stock, (ii) subdivide the
outstanding shares of Common Stock, or (iii) combine the outstanding shares of
Common Stock into a smaller number of shares, then in each such case the amount
set forth in the preceding sentence with respect to the exchange or change of
Series A Junior Preferred Shares shall be adjusted by multiplying such amount by
a fraction, the numerator of which is the number of shares of Common Stock
outstanding immediately after such event and the denominator of which is the
number of shares of Common Stock that were outstanding immediately prior to such
event.

     Section 8.  No Redemption.  The Series A Junior Preferred Shares shall not
                 -------------                                                 
be redeemable.

     Section 9.  Ranking.  The Series A Junior Preferred Stock shall rank junior
                 -------                                                        
to all other series of the Corporation's Preferred Stock as to the payment of
dividends and the distribution of assets, unless the terms of any such series
shall provide otherwise.

     Section 10.  Fractional Shares.  Series A Junior Preferred Shares may be
                  -----------------                                          
issued in fractions of a share which shall entitle the holder, in proportion to
such holder's fractional shares, to exercise voting rights, receive dividends,
participate in distributions and to have the benefit of all other rights of
holders of Series A Junior Preferred Shares.

     Section 11.  Amendment.  The Certificate of Incorporation of the
                  ---------                                          
Corporation shall not be further amended in any manner which would materially
alter or change the powers, preferences or special rights of the Series A Junior
Preferred Shares so as to affect them adversely without the affirmative vote of
the holders of a majority or more of the outstanding Series A Junior Preferred
Shares, voting separately as a class.

 
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<PAGE>
 
     IN WITNESS WHEREOF, the undersigned have executed and subscribed this
Certificate and do affirm the foregoing as true under penalties of perjury this
3rd day of December, 1996.


                                  /s/ Sam B. Humphries
                                  ------------------------- 
                                  Sam B. Humphries
                                  Chief Executive Officer



ATTEST:
/s/ Wesley G. Peterson  
----------------------------
Wesley G. Peterson
Chief Financial Officer




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